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ELEMENTARY LESSONS
ASTRONOMY.
ELEMENTARY LESSONS
m
ASTRONOMY.
J. NORMAN LOCKYER,
FELLOW OF THE ROVAL ASTRONOMICAL SOCIETY,
EDITOR OF "THE HEAVENS," ETC.
MACMILLAN AND CO.
1868.
[The right of translation and reproduction is reserved.]
LONDON :
R. CLAY, SON, AND TAYLOR, PRINTERS,
BREAD STREET HILL.
PREFACE.
THESE "Elementary Lessons in Astronomy" are in-
tended, in the main, to serve as a text-book for use
in Schools, but I believe they will be found useful to
" children of a larger growth," who wish to make them-
selves acquainted with the basis and teachings of one of
the most fascinating of the Sciences.
The arrangement adopted is new ; but it is the result
of much thought. I have been especially anxious in the
descriptive portion to show the Sun's real place in the
Cosmos, and to separate the real from the apparent
movements. I have therefore begun with the Stars, and
have dealt with the apparent movements in a separate
chapter.
It may be urged that this treatment is objectionable,
as it reduces the mental gymnastic to a minimum ; it
is right, therefore, that I should state that my aim
throughout the book has been to give a connected view
of the whole subject rather than to discuss any particular
parts of it ; and to supply facts, and ideas founded on
the facts, to serve as a basis for subsequent study and
discussion. A companion volume to the present one — I
allude to the altogether admirable " Popular Astronomy "
from the pen of the Astronomer Royal — may, from this
point of view, be looked upon as a sequel to two or three
chapters in this book.
vi PREFACE.
It has been my especial endeavour to incorporate the
most recent astronomical discoveries. Spectrum-analysis
and its results are therefore fully dealt with ; and distances,
masses, &c. are based upon the recent determination of
the solar parallax.
The use of the Globes and of the Telescope have both
been touched upon. Now that our best opticians are
employed in producing " Educational Telescopes," more
than powerful enough for school purposes, at a low price,
it is to be hoped that this aid to knowledge will soon
find its place in every school, side by side with the black-
board and much questioning.
All the steel plates in the book, acknowledged chefs-
d'ceuvres of astronomical drawing, have been placed at
my disposal by my friend Mr. Warren De La Rue.
I take this opportunity of expressing my thanks to
him, and also to the Council of the Royal Astrono-
mical Society, M. Guillemin, Mr. R. Bentley, the Rev.
H. Godfray, Mr. Cooke, and Mr. Browning, who have
kindly supplied me with many of the other illustrations.
I am also under obligations to other friends, espe-
cially to Mr. Balfour Stewart and Mr. J. M. Wilson, for
valuable advice and criticism, while the work has been
passing through the press.
J. N. L.
CONTENTS.
INTRODUCTION.
LESSON PACK
General Notions. — The Uses of Astronomy i
CHAPTER I.
THE STARS AND NEBULM.
I. — Magnitudes and Distances of the Stars. Shape of our
Universe , . . 9
II.— -The Constellations. Movements of the Stars. Movement of
our Sun 13
III.— Double and Multiple Stars. Variable Stars 18
IV.— Coloured Stars. Apparent Size. The Structure of the Stars.
Clusters of Stars 23
V. — Nebulae. Classification and Description 3*
VI.— Nebulae (concluded). Their Faintness. Variable Nebulae.
Distribution in Space, Their Structure. Nebular Hypo-
thesis 35
CHAPTER II.
THE SUN.
V I L— Its relative Brightness, its Size, Distance, and Weight ... 38
VIII.— Telescopic Appearance of the Sun-spots. Penumbra, Umbra,
Nucleus. Faculae. Granules. Red Flames ...... 45
IX.— Explanation of the Appearances on the Sun's Surface. The
Sun's Light and Heat. Sun-force. The Past and Future of
the Sun ........ 4 /..., 48
viii CONTENTS.
CHAPTER III.
THE SOLAR SYSTEM.
LESSON PAGE
X. — General Description. Distances of the Planets from the
Sun. Sizes of the Planets. The Satellites. Volume,
Mass, and Density of the Planets 54
XT.— The Earth. Its Shape. Poles. Equator. Latitude and
Longitude. Diameter 61
XII. — The Earth's Movements. Rotation. Movement round
the Sun. Succession of Day and Night 66
XIII.— The Seasons 7i
XIV. — Structure of the Earth. The Earth's Crust. Interior Heat
of the Earth. Cause of its Polar Compression. The
Earth once a Star f 77
XV. —The Earth (concluded}. The Atmosphere. Belts of
Winds and Calms. The Action of Solar and Terrestrial
Radiation. Clouds. Chemistry of the Earth. The
Earth's Past and Future . . . . ' 83
XVI.— The Moon : its Size, Orbit, and Motions : its Physical
Constitution 88
XVIt. — Phases of the Moon. Eclipses: how caused. Eclipses
of the Moon 95
XVIII.— Eclipses (concluded}. Eclipses of the Sun. Total Eclipses
and their Phenomena Corona. Red Flames .... 100
XIX.— The other Planets compared with the Earth. Physical
Description of Mars 104
XX. — The other Planets compared with the Earth (continued}.
Jupiter : his Belts and Moons. Saturn : general Sketch of
his System m
XXL— The other Planets compared with the Earth (concluded).
Dimensions of Saturn and his Rings. Probable Nature
of the Rings. Effects produced by the Rings on the
Planet Uranus. Neptune : its Discovery 116
CONTENTS. ix
LESSON PA<;E
XX 1 1.— The Asteroids, or Minor Planets. Bode's Law. Size of
the Minor Planets : their Orbits: how they are observed 120
XXIII.— Comets: their Orbits. Short-period Comets. Head, Tail,
Coma, Nucleus, Jets, Envelopes. Their probable Number
and Physical Constitution 123
XXIV. — Luminous Meteors. Shooting Stars. November Showers.
Radiant Points 130
XXV. —Luminous Meteors (concluded). Cause of the Phenomena
of Meteors. Orbits of Shooting Stars. Detonating
Meteors. Meteorites : their Classification. Falls.
Chemical and Physical Constitution 136
CHAPTER IV.
APPARENT MOVEMENTS OF THE HEAVENLY BODIES.
XXVI.— The Earth a moving Observatory. The Celestial Sphere.
Effects of the Earth's Rotation upon the apparent Move-
ments of the Stars. Definitions 142
XXVII.— Apparent Motions of the Heavens, as seen from different
parts of the Earth. Parallel, Right, and Oblique Spheres.
Circumpolar Stars. Equatorial Stars, and Stars invisible
in the Latitude of London. Use of the Globes . ... 147
XXVIII.— Position of the Stars seen at Midnight. Depends upon
the two Motions of the Earth. How to tell the Stars.
Celestial Globe. Star Maps. The Equatorial Constel-
lations. Method of Alignments 1 56
XXIX. — Apparent Motion of the Sun. Difference in Length be-
tween the Sidereal and Solar Day. Celestial Latitude
and Longitude. The Signs of the Zodiac. Sun's apparent
Path. How the Times of Sunrise and Sunset, and the
Length of the Day and Night, may be determined by
means of the Celestial Globe 165
XXX. — Apparent Motions of the Moon and Planets. Extreme
Meridian Heights of the Moon. Angle of her Path with
the Horizon at different Times. Harvest Moon. Varying
Distances, and varying apparent Size of the Planets.
Conjunction and Opposition 170
CONTENTS.
LESSON PAGE
XXXI. — Apparent Motions of the Planets (concluded). Elongations
and Stationary Points. Synodic Period, and Periodic
Time 176
XXXII. — Apparent Motions of the Planets (concluded). In-
clinations and Nodes of the Orbits. Apparent Paths
among the Stars. Effects on Physical Observations.
Mars. Saturn's Rings . , 182
CHAPTER V.
THE MEASUREMENT OF TIME.
XXXIII. — Ancient Methods of Measurement. 'Clepsydrae. Sun
Dials. Clocks and Watches. Mean Sun. Equation
of Time 190
XXXIV.— Difference of Time. How determined on the Terrestrial
Globe. Greenwich Mean Time. Length of the various
Days. Sidereal Time. Conversion of Time .... 198
XXXV.— The Week. The Month. The Year. The Calendar.
Old Style. New Style 202
CHAPTER VI.
LIGHT.— THE TELESCOPE AND SPECTROSCOPE.
XXXVI.— What Light is ; its Velocity ; how determined. Aberra-
tion of Light. Reflection and Refraction. Index of Re-
fraction. Dispersion. Lenses 207
XXXVII. — Achromatic Lenses. The Telescope. Illuminating Power.
Magnifying Power 214
XXXVIII.— The Telescope (concluded). Powers of Telescopes of
different Apertures. Large Telescopes. Methods of
Mounting the Equatorial Telescope 220
XXXI X. — The Solar Spectrum. The Spectroscope. Kirchhoff's
Discovery. Physical Constitution of the Sun .... 227
XL. — Importance of this Method of Research. Physical Con-
stitution of the Stars, Nebulas, Moon, and Planets.
Construction of the Spectroscope. Celestial Photography 233
CONTENTS. xi
CHAPTER VII.
DETERMINATION OF THE APPARENT PLACES OF THE
HEAVENLY BODIES.
LESSON PAGE
XLI. — Geometrical Principles. Circle. Angles. Plane and
Spherical Trigonometry. Sextant. Micrometer. The
Altazimuth and its Adjustment 239
XLII. — The Transit Circle and its Adjustments. Principles of its
Use. Methods of taking Transits. The Chronograph.
The Equatorial 249
XLHI. — Corrections applied to Observed Places. Instrumental
and Clock Errors. Corrections for Refraction and Aber-
ration. Corrections for Parallax. Corrections for Luni-
Solar Precession. Change of Equatorial into Ecliptic
Co-ordinates 258
XLI V.— Summary of the Methods by which True Positions of the
Heavenly Bodies are obtained. Use that is made of
these Positions. Determination of Time : of Latitude :
of Longitude „ 268
CHAPTER VIII.
DETERMINATION OF THE REAL DISTANCES AND
DIMENSIONS OF THE HE A VENLY BODIES.
XLV. — Measurement of a Base Line. Ordnance Survey. Deter-
mination of the Length of a Degree. Figure and Size
of the Earth. Measurement of the Moon's Distance . . 273
XLVI. — Determination of the Distances of Venus and Mars : of
the Sun. Transit of Venus. The Transit of 1882 . . . 280
XLVI I.— Comparison of the Old and New Values of the Sun's
Distance. Distance of the Stars. Determination of
Real Sizes 289
xii CONTENTS.
CHAPTER IX.
UNIVERSAL GRAVITATION.
LESSON PAGE
XLVIII. — Rest and Motion. Parallelogram of Forces. Law of
Falling Bodies. Curvilinear Motion. Newton's Dis-
covery. Fall of the Moon to the Earth. Kepler's Laws 293
X LI X.— Kepler's Second Law proved. Centrifugal Tendency.
Centripetal Force. Kepler's Third Law proved. The
Conic Sections. Movement in an Ellipse 302
L. — Attracting and Attracted Bodies considered separately.
Centre of Gravity. Determination of the Weight of the
Earth : of the Sun : of the Satellites 307
LI.— General Effect of Attraction. Precession of the Equinoxes :
how caused. Nutation. Motions of the Earth's Axis.
The Tides. Semi-diurnal, Spring, and Neap Tides.
Cause of the Tides. Their probable Effect on the Earth's
Rotation 315
APPENDIX , 327
INDEX 335
ILLUSTRATIONS.
PAGE
FRONTISPIECE : Spectra of the
Sun, Stars, and Nebula (to face
Title],
PLATE I. Star Clusters ... 27
II. Nebulae 31
IIL The Sun . . to face 38
IV. Sun-spots 44
. V. The Solar System . 54-55
VI. The Lunar Crater, Co-
pernicus . to face 94
VII. Eclipse of the Sun . . 102
PAGE
PLATE VIII. Mars in 1856, to face 104
,, IX. Mars in 1862 . . 109
„ X. Jupiter and Saturn,
to face 112
„ XI. Radiant - point of
Shooting Stars . 133
„ XII. Equatorial Tele-
scope .... 225
,, XIII. Spectroscope . . . 229
„ XIV. Portable Altazimuth 245
„ XV. Transit Circle . . .251
FIG. x. Orbit of a Double Star . 18
2. The Double-double Star
e Lyrae 19
3. Position of the Sun's axis . 41
4. Part of a Sun-spot, as
seen in a powerful tele-
scope 47
5. Section of the Plane of the
Ecliptic 56
6. Mode of constructing an
Ellipse 67
7. The Seasons 68
8. Explanation of the differ-
ent Altitudes of the
Sun in Summer and
Winter 72
9. 10, ii, 12. The Earth, as
seen from the Sun : —
At the Summer Solstice 73
,, Winter „ 74
,, Vernal Equinox 75
,, Autumnal ,, . 76
13. Cause of the Earth's sphe
roidal form ... 82
14. Phases of the Moon . 96
FIG. 15. General Theory of
Eclipses 98
16. General View of Jupiter
and his Moons . . .113
17. General View of Saturn
and his Moons . . .114
1 8. Ecliptic Chart .... 122
19. Donati's Comet (general
view) 125
20. Ditto, showing Head and
Envelopes 127
21. Fire-ball, as seen in a
telescope 138
22. A Parallel Sphere . . .148
23. A Right Sphere . . . . tb.
24. An Oblique Sphere . . 149
25. Southern Circumpolar
Constellations. . . .152
26. Northern Circumpolar
Constellations . . .153
27. The Great Bear at inter-
vals of six hours . . . 155
28. Equatorial Constella-
tions:—Orion . . . 162
29. Bootes . . .163
XIV
ILLUSTRA TIONS.
PAGE
FIG. 30. Equatorial Constella-
tions : — Perseus, Cas-
siopea . . 164
31. Sidereal and" Solar Days. 166
32. Harvest Moon .... 172
33. Retrogradations, Elonga-
tions, and Stationary
Points of Planets . .178
34. Path of Venus among the
Stars in 1868 .... 183
35. Path of Saturn among
the Stars, 1862-5 . .184
36. Orbits of Mars and the
Earth 185
37. Varying Appearances of
Saturn's Rings . . .187
38. Saturn when the Plane
of the Ring passes
through the Earth . .188
39. Ditto, when the North
Surface of the Rings is
visible ib.
40. Construction of the Sun-
dial 192
Aberration of Light . . 208
Atmospheric Refraction
41.
42.
209
43t Action of a Prism on a
beam of light. . . . 210
44. Action of two Prisms
placed base to base . .212
45. Action of a Convex Lens 213
46. Ditto, showing how the
Image is inverted . . ib.
47. Concave Lens . . . .215
48. Theory of the Astrono-
mical Telescope . . .217
.49. Star Spectroscope . . . 235
50. Direct - vision Spectro-
,scope 237
51. triangles 241
52. Ditto, with equal bases . 242
53. Trigonometrical Ratios . 243
PAGE
FIG. 54. Effect of the Aberration
of Light on a Star's ap-
parent place .... 260
55. Mode of Correction for
Aberration 261
56. Parallax 262
57. Transformation of Equa-
torial and Ecliptic Co-
ordinates 266
58. Measurement of the dis-
tance of the Moon . . 279
59. Ditto of Mars . . . .281
60. Transit of Venus . . . 283
61. Ditto, Sun's Disc, as seen
from the Earth . . . 285
62. Ditto, reversed .... ib.
63. Ditto, illuminated side of
the Earth at ingress . 286
64. Ditto, ditto, at egress . 287
65. Parallelogram of Forces . 294
66. Action of Gravity on the
Mjoon'spath .... 298
67. Kepler's Second Law . 300
68. Proof of ditto . . . .302
69. Circular Motion . . . 303
70. The Conic Sections . . 306
71. Orbital Velocities . . . 307
72. Centre of Gravity, in the
case of Equal Masses . 309
73. Ditto, in the case of
Unequal Masses . . . ib.
74. Fall of Planets to the Sun 310
75. The Cavendish Experi-
ment 312
76. Showing the effects of
Precession on the posi-
tion of the Earth's axis 318
77. Nutation 319
78. Apparent motion of the
Pole of the Equator
round the Pole of the
Heavens (or Ecliptic) . 320
ELEMENTARY LESSONS
ASTRONOMY.
INTRODUCTION.
GENERAL NOTIONS.— THE USES OF ASTRONOMY.
1. AT night, if the sky be cloudless, we see it spangled
with so many stars, that it seems impossible to count
them ; and we see the same sight whether we are in
England, or in any other part of the world. The earth
on which we live is, in fact, surrounded by stars on all
sides ; and this was so evident to even the first men who
studied the stars that they pictured the earth standing
in the centre of a hollow crystal sphere, in which the
r/ stars were fixed like golden nails.
2. In the daytime the scene is changed : in place of
thousands of stars, our eyes behold a glorious orb whose
rays light up and warm the earth, and this body we call
the »un. So bright are his beams that, in his presence, all
the " lesser lights," the stars, are extinguished. But if we
doubt their being still there we have only to take a candle
from a dark room into the sunshine to understand how
their feeble light, like that of the candle, is " put out " by
the greater light of the sun.
3. There are, however, other bodies which attract our
attention. The moon shines at night now as a cres-
cent and now as a full moon, sometimes rendering
the stars invisible in the same way as the sun does,
2 ASTRONOMY.
though in a less degree, and showing us by its changes
that there is some difference between it and the sun ;
for while the sun always appears round, because we receive
light from all parts of its surface turned towards us, the
shape of the bright or lit-up portion of the moon varies
from night to night, that part only being visible which is
turned towards the sun.
4. Again, if we examine the heavens more closely still,
we may see, after a few nights' watching, one, or perhaps
two, of the brighter " stars " change their position with
regard to the stars lying near them, or with regard to the
sun if we watch that body closely at sunrise and sunset.
These are the planets ; the ancients called them " wan-
dering stars."
5. But the planets are not the only bodies which move
across the face of the sky. Sometimes a comet may by
its sudden appearance and strange form awaken our
interest and make us acquainted with another class of
objects unlike any of those which we have previously
mentioned.
6. Such are the celestial bodies ordinarily visible to us.
Far away, and comparatively so dim that the naked eye
can make little out of them, lie the nebulae, so called
because in the telescope they often put on strange cloud-
like forms ; they differ as much from stars in their ap-
pearance as comets do from planets.
7. There are other bodies, to which we shall refer by
and by. But we will, in this place, content ourselves with
stating generally what Astronomy teaches us concerning
star and sun, moon and planet, comet and nebula.
8. To begin, then, with the stars. So far from being
fixed, and being stuck as it were in a hollow glass globe,
which state of things would cause all to be at pretty
nearly equal distances from us, they are all in rapid mo-
tion, and their distances vary enormously ; although
INTRODUCTION. 3
all of them are so very far away that they appear to us
to be at rest, as a ship does when sailing along at a
great distance from us. In spite, however, of their great
and varying distances, science has been able to get a
mental bird's-eye view of all the hosts of stars which
the heavens reveal to our eyes, as they would appear to
us if we could plant ourselves far on the other side of
the most distant one. The telescope — an instrument
which will be fully described further on— has, in fact,
taught us that all the stars which we see, form, after
all, but a cluster of islands as it were in an infinite
ocean of space ; so that we may think of all the stars
which we see, as forming our universe, and when we have
got that thought well into our minds we may think of
space being peopled with other universes, as there are
other towns besides London in England.
9. Further, we know that our sun is one of the stars
which compose this star-cluster, and that the reason
that it appears so much bigger and brighter than the
other stars is simply because it is the nearest star
to us.
We all of us know how small a distant house looks or
how feebly a distant gas-lamp or candle seems to shine ;
but the distant house may be larger than the one we live
in, or the distant light may really be brighter than the
one which, being nearer to us, renders the other insig-
nificant. It is precisely so with the stars. Not only
would they appear to us as bright as the sun, if we were
as near to them, but we know for a fact that some of
them are larger and brighter.
10. Now, why do the stars and the sun shine?
They shine, or give out light, because they are
•white hot. At their surfaces masses of metals and
other substances are burning together more fiercely than
anything we can imagine. They are globes of the fiercest
B 2
4 ASTRONOMY.
fire, compared to which a mass of white-hot iron is as
cold as ice,
11. What, then, are the planets? We may first state
that they are comparatively small bodies travelling round
our sun at various distances from him. Our earth is
one of them. A moment's thought on what we have said
about the sun and stars will, however, show us another
important difference between the planets and the sun. We
have seen that the sun is a white-hot body ; our earth, we
know, is, on the contrary, a cold one : all the heat we get
is from the sun. Because the earth is cold it cannot give
out light any more than a cold poker can. Astronomers
have learnt that all the other planets are like the earth in
this respect. They are all dark bodies — having no light
in themselves — and they all, like us, get their light and
heat from the sun. When, therefore, we see a planet in the
sky. we know that its light is sunshine second-hand ; that,
as far as its light is concerned, it is but a looking-glass
reflecting to us the light of the sun.
We have now got thus far: planets are dark,
or obscure, or non-self-luminous bodies travel-
ling round the sun, which is a bright body —
bright because it is white hot; and the sun is a
star, one of the stars which together form our
universe ; the reason that it appears larger and brighter
than the other stars being because we are nearer to it than
we are to the others. It seems likely that the other stars
have planets revolving round them, although astronomers
have as yet no positive knowledge on the matter, as they
are so very far away that the telescopes we possess at
present are not powerful enough to show us their planets,
if they have any.
12. We now come to the moon. What is it ? The
moon goes round the earth in the same way as we have
seen the planets revolving round the sun : it is in fact
INTRODUCTION. 5
a planet of the earth ; it is to the earth what the earth is
to the sun. Like the earth and planets, it is a dark body,
and this is the reason it does not always appear round
as the sun does. We only see that part of it that
is lit up by the sun. In the moon we have a speci-
men of a third order of bodies called satellites, or com-
panions, as they are the companions of the planets,
accompanying them in their courses round the sun.
We have then to sum up again — (i) the sun, a
star, like all the other stars in motion, (2) the
planets revolving round the sun, and (3) satel-
lites revolving round planets.
13. The nebulce and comets are quite distinct from
stars and planets, for they are masses of gas. The
nebulae lie far away from us, some of them perhaps out of
our universe altogether ; the comets rush for the most part
from distant regions to our sun, and having gone round
him they go back again, and we only see them for a small
part of their journey.
We saw in Art. 10 that the stars shone because they
are white hot ; so also nebulae and comets shine because
they are white hot.; but in the case of the stars we are
dealing with solid or liquid matter, while in the case
of the nebulae and comets we are dealing with burning
gas.
14-. Such, then, are some of the bodies with which the
science of ASTRONOMY has to deal ; but astronomers have
not rested content with the appearances of these bodies :
they have measured and weighed them in order to assign
to them their true place. Thus they have found out that
the sun is 1,260,000 times larger than the earth, and the
earth is 50 times larger than the moon. On the other
hand, as we have seen, they have discovered that, while
we travel round the sun, the moon travels round us, and
at a distance which is quite insignificant in comparison
6 ASTRONOMY.
In other words, the moon travels round us at a distance
of 240,000 miles, while we travel round the sun at a
distance of 91,000,000 miles.
15. We thus see how it is that the greater size of the
sun is balanced, so to speak, by its greater distance ; the
result being that the large distant sun looks about the
same size as the small near moon.
16. We already see how enormous are the distances
dealt with in astronomy, although they are measured in the
same way as a land-surveyor measures the breadth of
a river that he cannot cross. The numbers we obtain when
we attempt to measure any distance beyond our own
little planetary system convey no impression to the mind.
Thus the nearest fixed star is more than 19,000,000,000,000
miles away, the more distant ones so far away that light,
which travels at the rate of 186,000 miles in a second of
time, requires 50,000 years to dart from the stars to our
eyes !
17. In spite, however, of this immensity, the methods
employed by astronomers are so sure that, in the case of
the nearer bodies, their distances, sizes, weights, and
motions are now well known. We can indeed predict
the place that the moon — the most difficult one to deal
with — will occupy ten years hence, with more accuracy
than we can observe its position in the telescope.
18. Here we see the utility of the science, and how
upon one branch of it, PHYSICAL ASTRONOMY, which
deals with the laws of motion and the structure of the
heavenly bodies, is founded another branch, PRACTICAL
ASTRONOMY, which teaches us how their movements may
be made to help mankind.
19. Let us first see what it does for our sailors and
travellers. A ship that leaves our shore for a voyage
round the world takes with it a book called the " Nautical
Almanack," prepared beforehand— three or four years in
INTRODUCTION. 7
advance — by our Government astronomers. In this book
the places the moon, sun, stars, and planets will occupy
at certain stated hours for each day are given, and this
information is all our sailors and travellers require to
find their way across the pathless seas or unknown lands.
20. But we need not go on board ship or into new
countries to find out the practical uses of Astronomy.
It is Astronomy which teaches us to measure the flow
of time, the length of the day, and the length of the
year: without Astronomy to regulate them, clocks and
watches would be almost impossible, and quite useless.
It is Astronomy which divides the year into seasons for
us, and teaches us the times of the rising and setting of
the moon, which lights up our night. It is to Astronomy
that we must appeal when we would inquire into the early
history of our planet, or when we wish to map its surface.
21. Such, then, is Astronomy— the science which, as
its name, derived from two Greek words (ao-n'jp, " star,"
and i/o/xof, " law ") implies, unfolds to us the laws of the
stars.
CHAPTER I.
THE STARS AND NEBULA.
LESSON I.— MAGNITUDES AND DISTANCES OF THE
STARS. SHAPE OF OUR UNIVERSE.
22. THE first thing which strikes us when we look at
the stars is, that they vary very much in brightness.
All of those visible to the naked eye are divided into six
classes of brightness, called "magnitudes," so that we
speak of a very brilliant one as "a star of the first
magnitude:" of the feeblest visible, as a star of the
sixth magnitude, and so on. The number of stars of
all magnitudes visible to the naked eye is about 6,000 ;
so that the greatest number visible at any one time — as
we can only see one half of the sky at once — is 3,000.
If we employ a small telescope this number is largely
increased, as that instrument enables us to see stars too
feeble to be perceived by the eye alone. For this reason
such stars are called telescopic stars. The stars thus
revealed to us still vary in brightness, and the classifi-
cation into magnitudes is continued down to the I2th,
I4th, i6th, or even higher magnitudes, according to the
power of the telescope ; in powerful telescopes at least
20,000,000 stars down to the I4th magnitude are visible.
ro ASTRONOMY.
23. A star of the sixth magnitude is, as we have seen,
the faintest visible to the naked eye. It has been esti-
mated that the other stars are brighter than one of the
sixth magnitude, by the number of times shown in the
following table : —
Times.
A star of the 5th magnitude 2
„ 4th „ 6
„ 3d „ 12
„ 2d „ 25
„ ist „ 100
Sirius, the brightest of the )
ist magnitude stars . . ) 324
The Sun, the nearest star ^ ^
to us )
24. Now it is evident that these stars, as they all shine
out with such different lights, one star differing from
another star in glory, are either of the same size at very
different distances, the furthest away being of course the
faintest ; or are of different sizes at the same distance, the
biggest shining the brightest ; or are of different sizes at
different distances. Where the actual distances of the
stars are known we can be certain ; but from other con-
siderations it is most probable that the difference in
brilliancy is due to difference of distance, and not to size.
25. The distances of the stars from us are so great that
it scarcely conveys any impression on the mind to state
them in miles ; some other method, therefore, must be
used, and the velocity of light affords us a convenient
one. Light travels at the rate of 186,000 miles in a
second of time — that is to say, between the beats of the
pendulum of an ordinary clock, light travels a distance
equal to eight times round the earth.
THE STARS AND NEBULA. ir
26. In spite, however, of this great remoteness, the
distances of some of them are known with considerable
accuracy. Thus, leaving the sun out of the question, we
find that the next nearest is situated at a distance which
light requires three and a half years to traverse.
27. From the measurements already made, we may say
that, on the average, light requires fifteen and a half
years to reach us from a star of the first magnitude,
twenty-eight years from a star of the second, forty-three
years from a star of the third, and so on, until, for stars
of the 1 2th magnitude, the time required is 3,500 years.
28. Winding among the stars, a beautiful belt of pale
light spans the sky, and sometimes it is so situated, that
we see that it divides the heavens into two nearly equal
portions. This belt is the Milky Way; and the smallest
telescope shows that it is composed of stars so faint, and
apparently so near together, that the eye can only per-
ceive a dim continuous glimmer.
29. We find the largest stars scattered very irregularly,
but if we look at the smaller ones, we find that they
gradually increase in number as their position
approaches the portion of the sky occupied by
the Milky Way. In fact, of the 20,000,000 stars
visible, as we have stated, in powerful telescopes, at least
18,000,000 lie in and near the Milky Way. This fact
must be well borne in mind.
30. Adding this fact to what has been said about the
distances of the stars, we can now determine the shape
of our universe. It is clear that it is most extended
where the faintest stars are visible, and where they appear
nearest together; because they appear faint in conse-
quence of their distance, and because their close packing
does not arise from their actual nearness to each other,
but results from their lying in that direction at constantly
increasing distances. Indeed, the stars which give rise to
12 ASTRONOMY.
the appearance of the Milky Way, because in that part
of the heavens they lie behind each other to an almost
infinite distance, are probably as far from each other as
our sun is from the nearest star.
31. The Milky Way, then, indicates to us, and traces
for us, the direction in which our universe has
its largest dimensions; the absence of faint stars in
the parts of the sky furthest from the Milky Way shows
us that the limits of the universe in that direction are
much sooner reached than in the direction of the Milky
Way itself. We gather, therefore, that its thickness is
small compared with its length and breadth. This flat
stratum of stars is split, as we might split a round piece
of thick cardboard, in those regions where we see the
Milky Way divided into two branches, and here its
edge is double. Our sun is situated near the point at
which the mass of stars begins to divide itself into two
portions ; and, as there are more stars on the south side
of the Milky Way than there are on the north, we gather
that our earth occupies a position somewhat to the north
of the middle of its thickness.
32. But although the Milky Way thus enables us to get
a rough idea of the shape of our universe, as we might
get a rough idea of the shape of a wood from some point
within it by seeing in which direction the trees appeared
densest and thickest together, and in which direction it
was most easy to pierce its limits, still what the telescope
teaches us, and what we know of other similar universes,
shows that its boundaries are most probably very
irregular.
33. The MageUanic Clouds, called the Nubecula
Major and Nubecula Minor, visible in the southern
hemisphere, are two cloudy oval masses of light, and are
very like portions of the Milky Way, but they are
apparently unconnected with its general structure.
THE STARS AND NEBULA. 13
LESSON II. — THE CONSTELLATIONS. MOVEMENTS OF
THE STARS. MOVEMENT OF OUR SUN.
34. We have in the last lesson considered our star-
system as a whole ; we have discussed its dimensions,
and given an idea of its shape. Before we proceed
with a detailed examination of the stars of which it is
composed, it will be convenient to state the groupings
into which they have been arranged, and the way in
which any particular star may be referred to.
35. The stars then, from the remotest antiquity, have
been classified into groups called constellations, each
constellation being fancifully named after some object
which the arrangement of the stars composing it was
thought to suggest.
36. The first classification is due to Ptolemy of
Alexandria, who about the year 150 A.D., arranged the
1,022 stars observed by Hipparchus, the father of astro-
nomy, at Rhodes, about one century before our era.
His catalogue contains 48 constellations ; two were
added by Tycho Brahe. and to these 50 (called the
ancient] constellations have been added, in more
modern times, 59, carrying the number up to 109.
37- The names of the ancient constellations and of the
more important of the modern ones are as follow, begin-
ning with those through which the sun passes in his annual
round ; these are called the zodiacal constellations
(very carefully to be distinguished, as we shall see further
on (Art. 361), from the signs of the zodiac bearing the
same name). In English and in rhyme these are as
under :
" The Ram, the Bull, the Heavenly Twins,
And next the Crab, the Lion shines,
The Virgin and the Scales,
'4
ASTRONOMY.
The Scorpion, Archer, and He-goat,
The Man that bears the watering-pot,
And Fish with glittering tails."
And in Latin they run thus :
" Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra,
Scorpio, Sagittarius, Capricornus, Aquarius, Pisces.
38. The constellations visible above the zodiacal con-
stellations, called the northern constellations, are as
follow :
Ursa Major.
Ursa Minor.
Draco.
Cepheus.
Bootes.
Corona Borealis.
Hercules.
Lyra.
Cygnus.
Cassiopea.
Perseus.
A uriga.
Serpentarius.
Serpens.
Sagitta.
Aquila.
Delphinus.
Equuleus.
Pegasus.
Andromeda.
Triangulum.
Cameleoparda Us.
Canes Venatici.
Vulpecula et Anser.
Cor Caroli.
The Great Bear (The Plough).
The Little Bear.
The Dragon.
Cepheus.
Bootes.
The Northern Crown.
Hercules.
The Lyre.
The Swan.
Cassiopea (The Lady's Chair).
Perseus.
The Waggoner.
The Serpent Bearer.
The Serpent.
The Arrow.
The Eagle.
The Dolphin.
The Little Horse.
The Winged Horse.
Andromeda.
The Triangle.
The Cameleopard.
The Hunting Dogs,
The Fox and the Goose.
Charles' Heart.
THE STARS AND NEBULAE.
39. The constellations visible below the zodiacal ones,
called the southern constellations, are :
Get us.
Orion.
Eridanns.
Lepus.
Cants Major.
Can is Minor.
Argo Navis.
Hydra.
Crater.
Corvus.
Centaurus.
Lupus.
Ara.
Corona Austral is.
Piscis Australis.
Monoceros.
Columba Noachi.
Crux A ustralis.
The Whale.
Orion.
The River Eridanus.
The Hare.
The Great Dog.
The Little Dog.
The Ship Argo.
The Snake.
The Cup.
The Crow.
The Centaur.
The Wolf.
The Altar.
The Southern Crown.
The Southern Fish.
The Unicorn.
Noah's Dove.
The Southern Cross.
AO. The whole heavens, then, being portioned out into
these constellations, the next thing to be done was to in-
vent some method of referring to each particular star. The
method finally adopted and now in use is to arrange all
the stars in each constellation in the order of brightness,
and to attach to them in that order the letters of the
Greek alphabet, using after the letters the genitive of the
Latin name of the constellation. Thus Alpha (a) Lyra
denotes the brightest star in the Lyre ; a Ursa Minoris,
the brightest star in the Little Bear. Some of the
brightest stars are still called by the Arabian or other
names they were known by in former times, thus, a Lyrce
is known also as Vega, a Bootis as Arcturits, ft Orionis
as Rigel, a Ursa Mtnoris as Polaris (the Pole star), &c.
16
ASTRONOMY.
4-1. All the constellations, and the positions of the prin-
cipal stars, have been accurately laid down in Star-Maps
and on Celestial Globes. With one or other of these the
reader should at once make himself familiar. In star-
maps the stars are laid down as we actually see them
in the heavens, looking at them from the earth ; but in
globes their positions are reversed, as the earth, on which
the spectator is placed, is supposed to occupy the centre of
the globe, while we really look at the globe from the
outside. Consequently the positions of the stars are
reversed. So if we suppose two stars, the brighter one
of them to the right in the heavens, the brighter one
will be shown to the right of the other on a star-map,
but to the left of it on a globe.
4-2. The twenty brightest stars in the heavens, or first
magnitude stars, are as follow: they are given in the
order of brightness, and should be found on a map or
globe.
Sirius, in the constellation
Cam's Major.
Can opus, „
Argo.
Alpha, „
Centaur.
Arcturus, „
Bootes.
Rigel,
Orion.
Capella, „
Auriga.
Vega, „
Lyra.
Procyon, ,,
Canis Minor.
Betelgeuse, „
Orion.
Achernar, „
Eridanus.
Aldebaran, „
Taurus.
Beta, Centauri, „
Centaur.
Alpha. Crucis, „
Crux.
An tares, .,
Scorpio.
Atair, „
Aquila.
Spica, „
Virgo.
THE STARS AND NEBULAE. J?
Fomalhaut, in the constellation Piscis Australis.
Beta Crucis, „ Crux.
Pollux, „ Gemini.
Regulus, „ Leo.
43. Now, although the stars, and the various constel-
lations, retain the same relative positions as they did in
ancient times, all the stars are, nevertheless, in motion ;
and in some of them nearest to us, this motion, called
proper motion, is very apparent, and it has been
measured. Thus Arcturus is travelling at the rate of at
least fifty-four miles a second, or three times faster
than our Earth travels round the sun, which is one
hundred times faster than an ordinary railway train.
44. Nor is our Sun, which be it remembered is a
star, an exception ; it is approaching the constellation
Hercules at the rate of four miles in a second, carrying
its system of planets, including our Earth, with it Here,
then, we have an additional cause lor a gradual change
in the positions of the stars, for a reason we shall readily
understand, if. when we walk along a gas-lit street, we
notice the distant lamps. We shall find that the lamps
we leave behind close up, and those in front of us open
out as we approach them : in fact, the stars which our
system is approaching are slowly opening out, while
those we are quitting are closing up, as our distance from
them is Increasing.
45. The real motions of the stars, — called, as we have
seen, their proper motions, — and the one we have just
pointed out, however, are to be gathered only from the
most careful observation, made with the most accurate
instruments. There are apparent motions, which may
be detected in half an hour by the most careless
observer.
46. These apparent motions are caused, as we
C
1 8 ASTRONOMY.
shall fully explain by and by (Chap. IV.), by the two real
motions of the Earth, first round its own axis, and
secondly round the Sun.
LESSON III.— DOUBLE AND MULTIPLE STARS.
VARIABLE STARS.
47- A careful examination of the stars with powerful
telescopes, reveals to us the most startling and beautiful
appearances. Stars which ap-
pear single to the unassisted
eye, appear double, triple, and
quadruple, and in some in-
stances the number of stars
revolving round a centre com-
mon to all is even greater. Be-
cause our Sun is an isolated
star, and because the planets
. -Orbit of a Double Star. ^ nQW dark bodies> mstead
of shining, like the Sun, by their own light, as they once
must have done, it is difficult, at first, to realize such
phenomena, but they are among the most firmly-estab-
lished facts of modern astronomy. A beautiful star in the
constellation of the Lyra will at once give an idea of such a
system, and of the use of the telescope in these inquiries.
The star in question is (e) Lyras, and to the naked eye
appears as a faint single star. A small telescope, or
opera-glass even, suffices to show it double, and a power-
ful instrument reveals the fact that each star composing
this double is itself double ; hence it is known as " the
Double-double." Here, then, we have a system of four
suns, each pair, considered by itself, revolving round
THE STAXS AND NEBULAE.
Fit?. 2. --The Double-double Star
in the constellation Lyra. i. As
seen in an opera-glass. 2. As seen
in a small telescope. 3. As seen
in a telescope of great power.
a point situated between them; while the two pairs
considered as two single
stars, perform a much larger
journey round a point situ-
ated between them.
It may be stated roundly
that the wider pair will com-
plete a revolution in 2,000
years ; the closer one in half
that time ; and possibly both
double systems may revolve
round the point lying be-
tween them in something less
than a million of years.*
4-8. More than 6,000
double stars are now known,
and of these motion has already been detected in nearly
700, the motion in some cases being very rapid. In some
cases the brilliancy of the component stars is nearly equal,
but in others the light is very unequal. For instance,
a first magnitude star may have a companion of the four-
teenth magnitude. Sirius has, at least, one such com-
panion. Here is a-list of some double stars, showing the
time in which a complete revolution is effected :
Years.
Zeta (f) Her cults ;'" 36
Eta (77) Cor once Boreal is ... 43
Zeta (£) Cancri 60
Alpha (a) Centauri 75
Omega (a>) Leonis .......... ,r . 82
Gamma (7) Corona Boreal is 100
Delta (5) Cygni 1 78
Beta (/3) Cygni 500
Gamma (y) Leonis 1 200
* Admiral Sniyih.
C 2
20 ASTRONOMY.
49. Here, then, there can be no doubt that the stars are
connected, and such pairs are called physical couples,
to distinguish them from the optical couples, in which
the component stars are really distant from each other,
and have no real connexion ; their apparent nearness to
each other being an appearance caused by their lying in
the same straight line, as seen from the Earth.
50. Where the distance of a physical double star is
known, we can determine the dimensions of the orbit of
one star round the other, as we can determine the Earth's
orbit round the Sun. Thus we know that the distance
between the two stars of 61 Cygni is 4,275,000,000 miles,
and yet the two stars seem as one to the naked eye.
51. The stars are not only of different magnitudes
(Art. 22), but the brilliancy of some particular stars changes
from time to time. If the variation in the light is, as
it is generally, slow, regular, and within certain limits,
stars in which this is noticed are called variable stars,
or shortly, variables. In some cases, however, the increase
and decrease have been sudden, and in others the limits
of change have been unknown ; and hence we read of
new stars, lost stars, and temporary stars, in addition to
the more regular variables. There is little doubt, however,
that all these phenomena are the same in kind, though
different in degree.
52. The variation is, of course, determined by the
different magnitudes of the stars at different times, and
the amount of variability is measured by the extreme
magnitudes. The period of the variability is the
time that elapses between two successive greatest bright-
nesses.
53. We give a table of a few variable stars, in order
that the foregoing may be clearly understood :
THE STARS AND NEBULA 21
Change of Magnitude Period of
from to Change.
17 Argus ... I .... 4 ... 46 years.
R Cephei ... 5 .... n ... 73 years.
~ . , x- (lower than ) *f A^
R CasstopecE . . 6 . > . 435 days-
i or 2 . jlo^r^than
j.33,
$ Cancri ... 8 .... 10^. . . 10
2i . 4 2
54-. The fourth star on our list is a very interesting one,
for at its period of greatest brightness it sometimes reaches
the first magnitude, sometimes the second ; but among
the acknowledged variables )3 Persei is perhaps the most
interesting, as its period is so short, and, unlike o Ceti—
(called also Mira, or the Marvellous) — it is never invisible
to the naked eye. The star in question shines as a star
of the second magnitude for two days and thirteen hours
and a half, and then suddenly loses its light and in three
hours and a half falls to the fourth magnitude ; its
brilliancy then increases again, and in another period
of three hours and a half it reattains its greatest bright-
ness— all the changes being accomplished in less than
three days.
55. Among the new, or temporary stars, those ob-
served in 1572 and last year (1866) are the most notice-
able. The first appeared suddenly in the sky and was
visible for seventeen months ; its light at first was equal
to that of the planets at their greatest brilliancy ; so bright
was it indeed, that it was clearly visible at noonday. Now
it is not a little curious that in the years 945 and 1264
something similar was observed in the same region of the
sky (in Cassiopea) in which this star appeared. If then
22 ASTRONOMY.
we assume all these phenomena to be due to the fact that
we have here a long-period variable star which is very
bright at its maximum and fades out of view at its mini-
mum, we may expect a reappearance of the star in the
year 1885.
56. We now come to the new star which broke upon
our sight last year, in the constellation of Corona Bo-
r?alis, and which was observed with much minuteness ami
with powerful methods of research not employed before.
This star was recorded some years ago as one of the
ninth magnitude. In May, however, it suddenly flashed
up, and on the I2th of that month shone as a star of the
second magnitude. On the 14th it had descended to the
third magnitude, — the decrease of brightness was for some
time at the rate of about half a magnitude a day, and
towards the end of May it was less rapid. There is good
reason to believe that this increased brilliancy was due to
the sudden ignition of hydrogen gas in the star's atmo-
sphere. Here we have a fact which must prove of the
highest importance, although we are not yet in a position
to do much more than speculate upon it.
57. The question of variable stars is one of the most
puzzling in the whole domain of astronomy. Mr. Balfour
Stewart, from his researches on the Sun — which is doubt-
less a variable star — thinks that " we are entitled to
conclude that, in our own system, the approach of a
planet to the Sun is favourable to increased brightness,
and especially in that portion of the Sun which is next
the planet." In the case of variable stars, the hypothesis
which was formerly thought to give the best explanation
of the phenomenon is that which assumes rotation on an
axis, while it is supposed that the body of the star is not
equally luminous on every part of its surface
58. If, instead of this, we suppose such a star to have
a large planet revolving round it at a small distance, then,
THE STARS AND NEBULA. 23
according to Mr. Stewart's theory, that portion of the star
which is near the planet will be more luminous than that
which is more remote ; and this state of things will revolve
round as the planet itself revolves, presenting to a distant
spectator an appearance of variation, with a period equal
to that of the planet.
59. If we suppose the planet to have a veiy elliptical
orbit, then for a long period of time it will be at a great
distance from its primary, while, for a comparatively short
period, it will be very near. We should, therefore, expect
a long period of darkness, and a comparatively short one
of intense light — precisely what we have in temporary
stars.
LESSON IV.— COLOURED STARS. APPARENT SIZE. THE
STRUCTURE OF THE STARS. CLUSTERS OF STARS.
6O. The stars shine out with variously coloured lights;
thus we have scarlet stars, red stars, blue and green
stars, and indeed stars so diversified in hue that ob-
servers attempt in vain to define them, so completely
do they shade into one another. Of large stars oi
different colours we may give the following table, founded
on Mr. Ennis's observations : —
Red Stars . . . Aldebaran. Antares. Betelgeuse.
Blue Stars . . . Capella. Rigel. Bellatrix. Pro-
cyon. Spica.
Green Stars . . Sirius. Vega. A fair. Deneb.
Yellow Stars . . Arcturus.
White Stars . . Regulus. Denebola. Fomalhaut.
Polaris.
24 ASTRONOMY.
61. In the double and multiple stars, however, we meet
with the most striking colours and contrasts ; Iota (i)
Cancri, and Gamma (y) Andromeda;, may be instanced.
In Eta (77) Cassiopece we find a large white star with
a rich ruddy purple companion. Some stars occur of
a red colour, almost as deep as that of blood. What
wondrous colouring must be met with in the planets lit
up by these glorious suns, especially in those belonging
to the compound systems, one sun setting, say in clearest
green, another rising in purple or yellow or crimson ; at
times two suns at once mingling their variously coloured
beams ! A remarkable group in the Southern Cross pro-
duced on Sir John Herschel "the effect of a superb piece
of fancy jewellery." It is composed of over 100 stars,
seven of which only exceed the tenth magnitude ; among
these, two are red, two green, three pale green, and one
greenish blue.
62. The colours of the stars also change. If we go
back to the times of the ancients, we read that Sirius,
which is now green, was red ; that Capella, which is now
pale blue, was also red.
63. In some variable stars the changes of colours
observed are very striking. In the new star of 1572,
Tycho Brahe observed changes from white to yellow, and
then to red ; and we may add that generally when the
brightness decreases the star becomes redder.
64-. The size or diameter of the stars cannot be deter-
mined by our most powerful instruments ; but we know
that, as seen from the Earth, they are, in consequence
of their distance, mere points of light, so small as to be be-
yond all our most delicate measurement. The Moon, which
travels very slowly across the sky, sometimes (as we shall
see by and by) gets before, or eclipses, or occults, some
of them ; but they vanish in a moment —which they would
not do if they were not as small as we have stated.
THE STARS AND NEBULA. 25
65. We will now pass on to what is known of the
physical constitution of the stars. In the first place we
know that the stars, of whatever their interiors may be
composed, present to us on their exteriors a bright surface,
which is called the photosphere; outside this photo-
sphere, as outside the surface of our earth, is an atmo-
sphere composed of vapours. The materials of the
photospheres are at an intense heat : so hot are they,
that, although they consist of metals and other substances,
they exist in a liquid or vaporous state — these states being
the effect of heat.
66. We can render this intelligible by taking water
and iron as instances : when both are in a solid state
we get ice and hard iron ; if we apply heat we melt both
ice and hard iron into water and molten iron — we know
that it requires more heat to melt iron than it does to melt
ice. Having got both into a liquid state, additional heat will
turn the water into steam and the molten iron into iron-
vapour ; but again the heat required to vaporize the iron
is vastly greater than that required to turn the water into
steam — how much greater may be gathered from the fact
that while ice melts at o° of the centigrade thermometer,
iron only melts at 2,000°: the heat required to produce
iron-steam or vapour is not known.
67. The degree of heat therefore present in the photo-
spheres of the stars exceeds our measurement. Do we
know anything of the substances which throw out this
heat and therefore light ? Yes, a little. For instance : —
Beta O) Pcgasi contains sodium, magnesium, and perhaps
barium.
Sirius „ sodium, magnesium, iron, and
hydrogen.
Alpha (a) Lyra (Vega) sodium, magnesium, and iron.
Pollux contains sodium, magnesium, and iron.
26 ASTRONOMY.
68. Now the vapours produced in the photospheres
ascend to form the atmospheres, and these atmospheres
absorb the light given out by the photospheres. A piece
of coloured glass will teach us what absorption is. Thus
a green glass is green because it absorbs all other light
but the green ; it is a sort of sieve, which stops every ray
of light except the green ones. So on with glasses, solids,
vapours, or liquids of other colours. Now the colours of
the stars may be influenced not only by the degree of
heat of their photospheres, but in the amount of absorp-
tion produced by their atmospheres. Our Sun at setting,
for instance, seems sometimes blood red, in consequence
of the absorption of our atmosphere ; if the absorption
were in his own atmosphere, he would be blood red
at noonday. Concerning the causes which produce the
changes, both in colour and brightness, we must confess
that, after all, we are yet ignorant.
69. It is remarkable that the elements most widely
diffused among the stars, including hydrogen, sodium,
magnesium, and iron, are some of those most closely
connected with the living organisms of our globe.
We shall be able, when we come to examine the struc-
ture of the nearest star— the Sun — to obtain a more
detailed knowledge of the structure of the stars generally.
70. Having now dealt with the peculiarities of indi-
vidual stars, — that is to say, their distance, arrangement,
colour, variability, and structure, — we next come to the
various assemblages or companies of stars observed in
various parts of the heavens.
71. In the double and multiple systems (Art. 47) we
saw the first beginnings of the tendency of the stars to
group themselves together. In some parts of our system
this tendency is exhibited in a very remarkable manner,
the beautiful group of the Pleiades affording a familiar
instance. The six or seven stars visible to the naked eye
Plate I.
STAR-CLUSTERS.
i. The Cluster in Hercules. 2. The Crab Cluster.
THE STARS AND NEBULA. 29
become 60 or 70 when viewed in the telescope. The
Hyades, in the constellation Taurus, and the Prsesepe, or
" Beehive," in Cancer, may also be mentioned. In other
cases the groups consist of an innumerable number of
suns apparently closely packed together. That in the
constellation Perseus is among the most beautiful objects
in the heavens ; but many others, scarcely less stupen-
dous, though much fainter by reason of the greater
distance, are revealed by the telescope.
72. Assemblages of stars are divided into—
1. Irregular group*, generally more or less visible
to the naked eye.
2. Star-clusters, invisible to the naked eye, but
which, in the most powerful
telescopes, are seen to consist
of separate stars. These are
sub-divided into ordinary
clusters, and globular
clusters.
73. Clusters and nebulae are designated by their num-
ber in the catalogues which have been made of them by
different astronomers. The most important of these
catalogues have been made by Messier, Sir William
Herschel, and Sir John Herschel. A catalogue recently
published by the latter contains 5,079 objects.
74-. We have already given some examples of star-
groups. The magnificent star-clusters, in the constel-
lations Hercules, Libra, and Aquarius, may be instanced as
among those which are best seen in moderate telescopes ;
but some of the clusters which lie out of our universe,
and which we must regard as other universes, are at such
immeasurable distances, and are therefore so faint, that
in the most powerful telescopes the real shape and boun-
30 AXTKONOMY.
clary are not seen, and there is a gradual fading away
at the edge, the last traces of which appear either as a
luminous mist, or cloud-like filament, which become finer
till they cease altogether to be seen. The Dumb-Bell
cluster, in Vulpecula, and the Crab cluster, in Taurus,
both of which have been resolved into Stars, are instances
of this.
75. In some of these star-clusters the increase of bright-
ness from the edge to the centre is so rapid that it would
appear that the stars are actually nearer together at the
centre than they are near the edge of the cluster ; in fact,
that there is a real condensation towards the centre.
LLSSON V. — NEBUL/E. CLASSIFICATION AND
DESCRIPTION.'
76. We now come to the Nebulae. " Nebula " is a
Latin word signifying a cloud, and for this reason the
name has been given to everything which appeared cloud-
like to the naked eye or in a telescope. The group in
Perseus, for instance, appears like a nebula to the naked
eye ; in the smallest telescope, however, it is separated
into stars.
77. Every time a telescope larger than any formerly
used has been made use of, however, numbers of what
were till then called nebulae, and about which as nebulas
nothing was known, have been found to be nothing but
star-clusters, some of them of very remarkable forms, so
distant that even in telescopes of great power they could
not be resolved,— that is to say, could not be separated
into distinct stars.
Plate ft.
i. The Nebula in Orion
NEBUL/E.
2. Spiral Nebula in Canes Venatici.
THE STARS AND NEBULAE. 33
78. Now, this is what has happened ever since the dis-
covery of telescopes. Hence it was thought by some that
all the so-called nebulae were, in reality, nothing but
distant star-clusters.
79. One of the most important discoveries of modern
times, however, has furnished evidence of a fact long ago
conjectured by some astronomers, — namely, that some of
the nebulae are something different from masses of stars,
and that the cloud-like appearance is due to something
else besides their distance and the still comparatively
small optical means one can at present bring to bear upon
them.
80. This discovery is so recent that there has not yet
been time to sort out the real nebulae from those which,
by reason of their great distance, appear like nebulae. We
are compelled, therefore, in this book to accept as nebulae
all formerly classed as such which up to this time have
not been resolved into stars.
81. Nebulae, then, may be divided into the following
classes: —
1.— Irregular netulse.
2.— Ring- nebulae and Elliptical nebulse.
3.— Spiral, or Whirlpool nebulae.
4-.— Planetary nebulae.
5. Nebulae surrounding stars.
82. Some of the irregular nebulae — those in the
constellations Orion and Andromeda, for example — are
visible to the naked eye on a dark night.
83- The great nebula of Orion is situated in the part of
the constellation occupied by the sword-handle and sur-
rounding the multiple-star Theta (6). The nebulosity near
the stars is fiocculent, and of a greenish white tinge. There
seems no doubt that the shape of this nebula and the
position of its brightest portions are changing. One part
of it appears, in a powerful telescope, startlingly like
D
34 ASTRONOMY.
the head of a fish. On this account it has been termed
the Fish-mouth nebula.
84-, Two other fine irregular nebulae are visible in
the Southern hemisphere : one is in the constellation
Dorado, the other surrounds Eta (rj) Argus. The latter
occupies a space equal to about five times the apparent
area of the Moon.
85. We have classed the ring-nebulae and elliptical
nebulae together because probably the latter are, in several
instances, ring-nebulae looked at sideways. The finest
ring-nebula is the 57th in Messier's catalogue (written
57 M. for short). It is in the constellation Lyra. The
finest elliptical nebula is the one in Andromeda to which
we have before referred. This nebula, the 3ist of Messier's
catalogue (31 M.), when viewed in large instruments,
shows several curious black streaks running in the direc-
tion in which the npbula is longest.
86. The spiral or whirlpool nebulae are repre-
sented by that in the constellation of Canes Venatici
(51 M.). In an ordinary telescope this presents the ap-
pearance of two globular clusters, one of them surrounded
by a ring at a considerable distance, the ring varying in
brightness, and being divided into two in a part of its
length. But in a larger instrument the appearance is en-
tirely changed. The ring turn. s. into a spiral coil of nebulous
matter, and the outlying mass is seen connected with the
main mass by a curved band. 33 M. Piscium, and 99 M.
Virginis, are other examples of this strange phenomenon,
which indicate to us the action of stupendous forces of a
kind unknown in our own universe,
87. The fourth class, or planetary nebulae, were
so named by Sir John Herschel, as they shine with a
planetary and often bluish light, and are circular or
slightly elliptical in form. 97 M. Ursae Majoris and
46 M. Argus may be taken as specimens.
THE STARS AND NEBULA. 35
88. We come lastly to the nebuhe surrounding
stars, or nebulous stars. The stars thus surrounded
are apparently like all other stars, save in the fact of the
presence of the appendage ; nor does the nebulosity give
any signs of being resolvable with our present telescopes.
Iota (i) Orionis, Epsilon (*) Orionis, 8 Canum Venati-
corum, and 79 M. Ursae Majoris, belong to this class.
LESSON VI. — NEBULAE (continued}. THEIR FAINT-
NESS. VARIABLE NEBULAE. DISTRIBUTION IN SPACE.
THEIR STRUCTURE. NEBULAR HYPOTHESIS.
89. Having stated and described the several classes
into which nebulae may be divided, their general features
and structure have next to be considered.
90. Like the stars, they are of different brightnesses,
but as yet they have not been divided into magnitudes.
This, however, has been done in a manner by determining
what is termed the space-penetrating power or
light-g rasping power of the telescope powerful enough
to render them visible. Thus, supposing nebulae to con-
sist of masses of stars, it has been estimated that Lord
Rosse's great Reflector, the most powerful instrument as
yet used in such inquiries, penetrates 500 times further
into space than the naked eye can ; that is, can detect
a nebula or cluster 500 times further off than a star of the
sixth magnitude.
91. Now, if we suppose that a sixth magnitude star is
12 times further off than a star of the first magnitude —
and this is within the mark — and that, as we have seen in
Art. 27, light requires 1 20 years to reach us from such a
star, the telescope we have referred to penetrates so pro-
foundly into space that no star can escape its scrutiny,
D 2
36 ASTRONOMY.
" unless at n remoteness that would occupy light in over-
spanning it sixty thousand years."
92. An idoa of the extreme faintness of the more dis-
tant nebulas may be gathered from the fact, that the light
of some of those visible in a moderately-large instrument
has been estimated to vary from y^ to siroo~o °f ^e
light of a single sperm candle consuming 158 grains of
material per hour, viewed at the distance of a quarter
of a mile: that is, such a candle a quarter of
a mile off is 20,000 times more brilliant than
the nebula !
93. The phenomenon of variable, lost, new, and tempo-
rary stars has its equivalent in the case of the nebulae, the
light of which, it has been lately discovered, is in some
cases subject to great variations.
94-. In 1 86 1 it was found that a small nebula, dis-
covered in 1856 in Taurus, near a star of the tenth magni-
tude, had disappeared, the star also becoming dimmer.
In the next year the nebula increased in brightness again.
The compressed nebula 80 M. in May 1860, appeared as
a star of the seventh magnitude. During the next month
it recovered its nebulous appearance.
95. In Art. 30 the marked character of the distribution
of the stars of our universe, giving rise to the appearance
of the Milky Way, was pointed out. The distribution of
the nebulae, however, is very different ; in general they
lie out of the Milky Way, so that they are either less con-
densed there, or the visible universe (as distinguished
from our own stellar one) is less extended in that
direction. They are most numerous in a zone which
crosses the Milky Way at right angles, the constellation
Virgo being so rich in them that a portion of it is termed
the nebulous region of Virgo. In fact, not only is the
Milky Way the poorest in nebulae, but the parts of the
heavens furthest away from it are richest.
THE STARS AND NEBULA. 37
96. We now come to the question, What is a Nebula ?
Theanswer is— A true nebula is a mass of glowing
or incandescent gas, and there are indications that
the gases in question are nitrogen and hydrogen. This
fact, the fruit of the brilliant discovery which has been
before alluded to (Art. 79), for ever sets at rest the ques-
tion so long debated as to the existence or non-existence
of a nebulous fluid in space.
97. When therefore we see, in what we know to be
a true nebula, closely associated points of light, we must
not regard the appearance as an indication of resolvability
into true stars. These luminous points, in some nebulas
at least, must be looked upon as themselves gaseous
bodies, denser portions probably of the great nebulous
mass. It has been suggested that the apparent perma-
nence of general form in a nebula is kept up by the
continual motions of these denser portions.
98. The nebular hypothesis, given to the world
before the existence of a nebulous fluid was proved,
supposes that all the countless suns which are distributed
through space once existed in the condition of nebulous
matter. It may take long years to prove, or disprove,
this hypothesis ; but it is certain that the tendency of
recent observations is to show its correctness.
CHAPTER II.
THE SUN.
LESSON VII. — ITS RELATIVE BRIGHTNESS, ITS SIZE,
DISTANCE, AND WEIGHT.
99. WE will now consider the star nearest to us —
the Sun, which dazzles the whole family of planets by its
brightness, supports their inhabitants by its heat, and
keeps them in bounds by its weight.
100. The relative brilliancy of the centre of our
system, compared to that of the stars, is, as we saw in
Art. 23, so great that it is difficult at first to look upon it
as in any way related to those feeble twinklers. This
difficulty, however, is soon dispelled when we consider
how near it is to us. Thus, to give another instance,
though we receive 10,000,000,000 times more light from
the Sun than we do from Alpha (a) Lyra, that star is
more than a million times further from us. There is
reason to believe, indeed, that our Sun is, after all, by no
means a large star compared with others ; for if we assume
that the light given out by Sirius, for instance, is no more
brilliant than is our sunshine, that star would be equal in
bulk to more than 3,000 suns.
101. Astronomers now know the distance of the Sun
from the Earth. It is about 91,000,000 miles ; and it is
Plate IE
p
m
a.
< I
O
o a
o
THE SUN. 39
easy, therefore, as we shall see by and by (Chap. VIII.), to
determine its size ; and here again, as in the case of the
distances of the stars, we arrive at figures which convey
scarcely any ideas to the mind. The distance from one
side of the Sun to the other, through its centre — or, in
other words, the diameter of the Sun, — is 853,380 miles.
Were there a railway round our earth, a train, going at
the rate of 30 miles an hour, would accomplish the journey
in a month • a railway journey round the Sun, going at the
same rate, would require more than nine years. In this
way we may also obtain the best idea of the Sun's distance
from us — a distance travelled over by light in eight and a
half minutes. A train going at the speed we have named,
and starting on the 1st of January, 1867, would not arrive
at the Sun till about the middle of the year 2,205 •
102. Such then are the distance and size of the centre
of our system. If we represent the Sun by a globe about
two feet in diameter, a pea at the distance of 430 feet will
represent the Earth ; and let us add, the nearest fixed star
would be represented by a similar globe placed at the
distance of 9,000 miles.
103. More than 1,200,000 Earths would be required to
make one Sun. Astronomers express this by saying that
the volume of the Sun is 1,200,000 times greater than that
of the Earth ; but as the matter of which the Sun is
composed weighs only one quarter as much, bulk for bulk,
as do the materials of which the Earth is made up, taken
together, 300,000 Earths only would be required in one
scale of a balance to weigh down the Sun in the other.
That is, the mass, or weight of the Sun, is 300,000 times
greater than that of our Earth.
104. The Sun, like the Earth or a top when spinning,
turns round, or rotates, on an axis; this rotation was
discovered by observing the spots on its surface, about
which we shall have much to say in the next Lesson. It
40 ASTRONOMY.
is found that the spots always make their first appear-
ance on the same side of the Sun ; that they travel across
it in about fourteen days ; and that they then disappear
on the other side. This is not all : if they be observed
in June, they go straight across the sun's face or disc
with a dip downwards ; if in September, they then cross
in a curve ; while in December they go straight across
again, with a dip upwards r and in March their paths are
again curved, this time with the curve in the opposite
direction.
105. Now it is important that we make this perfectly
clear. We know that the Earth goes round the Sun once
a year. It has been found also that its path is so level
— that is to say, the Earth in its journey does not go up
or down, but always straight on — that we might almost
imagine the Earth floating round the Sun on a boundless
ocean, both Sun and Earth being half immersed in it. We
shall see further on that this level — this plane— called the
plane of the Ecliptic — is used by astronomers in precisely
the same way as we commonly use the sea level. We
say, for instance, that such a mountain is so high above
the level of the sea. Astronomers say that such a star
is so high above the plane of the ecliptic.
106. Well then, we have imagined the Earth and Sun
to be floating in an ocean up to the middle — which is the
meaning of half immersed. Now, if the Sun were quite
upright, the spots would always seem at the same distance
above the level of our ocean. But this we have not found
to be the case. From two opposite points of the Earth's
path (the points it occupies in June and December) the spots
are seen to describe straight lines across the disc, while
midway between these points (September and March)
their paths are observed to be sharply curved, in one case
with the convex side upwards, in the other with the con-
vex side downwards. A moment's thought will show that
THE SUN. 41
these appearances can only arise from a dipping down of
the Sun's axis of rotation. Now this we find to be the
September. December. March.
J''ig: 3. — Position of the Sun's axis, and apparent paths of the spots across
the disc, as seen from the Earth at different times of the year. The arrows
show the direction in which the Sun turns round.
case. The Sun's axis inclines towards the point occu-
pied by the Earth in September. When we come to deal
with the Earth and the other planets, we shall find that
their axes also incline in different directions.
1O7. It has been found that the spots, besides having
an apparent motion, caused by their being carried round
by the Sun in its rotation, have a motion of their own.
This proper motion, as distinguished from their apparent
motion, has recently been investigated in the most com-
plete manner by Mr. Carrington. What he has dis-
covered shows that there need be no wonder that different
observers have varied so greatly in the time they have
assigned to the Sun's rotation. As we have already shown
(Art. 104), this rotation has been deduced from the time
taken by the spots to cross the disc ; but it now seems that
all sun-spots have a movement of their own, and that the
rapidity of this movement varies regularly with
their distance from the solar equator,— that is,
the region half-way between the two poles of rotation. In
42 ASTRONOMY.
fact, the spots near the equator travel faster
than those away from it, so that if we take an equa-
torial spot we shall say that the Sun rotates in about
twenty-five days ; and if we take one situated halt-way
between the equator and the poles, in either hemisphere,
we shall say that it rotates in about twenty-eight days.
1O8. We have now considered the distance and size of
the Sun ; we have found that it, like our Earth, rotates
on its axis, and we have determined the direction in which
the axis points. We must next try to learn something of
its appearance and of its nature, or, as it is called, its
physical constitution. Here we confess at once that
our knowledge on this subject is not yet complete. This,
however, is little to be wondered at. We have done so
much, and gleaned so many facts, at distances the very
statement of which is almost meaningless to us, so stupen-
dous are they, that we forget that our mighty Sun, in spite
of its brilliant shining and fostering heat, is still some
91,000,000 miles removed ;— that its diameter is 100 times
that of our Earth ; and that the chasm we call a sun-
spot is yet large enough to swallow us up, and half a
dozen of our sister planets besides ; while, if we employ
the finest telescope, we can only observe the various
phenomena as we should do with the naked eye at a
distance of 180,000 miles.
To look at the Sun through a telescope, without proper
appliances, is a very dangerous affair. Several astro-
nomers have lost their eyesight by so doing, and our
readers should not use even the smallest telescope without
proper guidance.
Plat*
SUN-SPOTS (the great Sun-Spot of 1865).
The spot entering the Sun's disc, Oct. 7th (foreshortened \iew). 2. Oct iDth.
3. Oct. i4th : central view, showing the formation of a bridge, and the
nucleus. 4. Oct. i6th.
THE SUN. 45
LESSON VIII.— TELESCOPIC APPEARANCE OF THE SUN-
SPOTS. PENUMBRA, UMBRA, NUCLEUS. FACUL/E.
GRANULES. RED FLAMES.
1O9. We have already said that the first things which
strike us on the Sun's surface, when we look at it with a
powerful telescope, are the spots. In Plate IV. we give
drawings of a very fine one, visible on the Sun in 1865. We
shall often refer to them in the following description. The
spots are not scattered all over the Sun's disc, but are
generally limited to those parts of it a little above and
below the Sun's equator, which is represented by the
middle lines in Fig. 3. The arrows show the direction in
which the spots, carried round by the Sun's rotation, appear
to travel across the disc.
HO. The spots float, as it were, in what, as we have
already seen in the case of the stars, is called the photo-
sphere; the half-shade shown in the spot is called the
penumbra (that is, half shade) ; inside the penumbra is
a still darker shade, called the umbra, and inside this
again is the nucleus. Diagrams 3 and 4 of Plate IV.
will render this perfectly clear. The white surface repre-
sents the photosphere; the half tones the penumbra;
the dark, irregular central portions the umbra; and the
blackest parts in the centre of these dark portions, the
nucleus.
ill- Sun-spots are cavities, or hollows, eaten
into the photosphere, and these different shades
represent different depths.
112. Diligent observation of the umbra and penumbra,
with powerful instruments, reveals to us the fact that
change is going on incessantly in the region of the spots.
46 ASTRONOMY.
Sometimes changes are noticed, after the lapse of an hour
even : here a portion of the penumbra is seen setting
sail across the umbra ; here a portion of the umbra is
melting from sight ; here, again, an evident change of
position and direction in masses which retain their form.
The enormous changes, extending over tens of thousands
of square miles of the Sun's surface, which took place in
the great sun-spot of 1865, are shown in Plate IV.
113. Near the edge of the solar disc, and especially
about spots approaching the edge, it is quite easy, even
with a small telescope, to discern certain very bright
streaks of diversified form, quite distinct in outline, and
either entirely separate or uniting in various ways into
ridges and network. These appearances, which have been
termed faculee, are the most brilliant parts of the Sun.
Where, near the edge, the spots become invisible, undu-
lated shining ridges still indicate their place — being more
remarkable thereabout than elsewhere, though everywhere
traceable in good observing weather. Faculae may be
of all magnitudes, from hardly visible, softly-gleaming,
narrow tracts 1,000 miles long, to continuous compli-
cated and heapy ridges 40,000 miles and more in length,
and 1,000 to 4,000 miles broad. Ridges of this kind
often surround a spot, and hence appear the more con-
spicuous ; such a ridge is shown in Fig i, Plate IV. ;
but sometimes there appears a very broad white platform
round the spot, and from this the white crumpled ridges
pass in various directions.
114-. So much for the more salient phenomena of the
Sun's surface, which we can study with our telescopes.
There is much more, however, to be inquired into ; and here
we may remark that the Sun himself has bestowed a great
boon upon observational Astronomy ; and, whether brightly
shining or hid in dim eclipse, now tells his own story, and
prints his image on a retina which never forgets, and withal
THE SUN. 47
so docilely, that each day he is visible at the Kew Obser-
vatory a young lady 'takes observations which surpass
immeasurably in value those made by the hardest-headed
astronomers of bygone times.
115. We may begin by saying, that the whole surface of
the Sun, except those portions occupied by the spots, is
coarsely mottled; and, indeed, the mottled appearance
requires no very large amount of optical power to render
it visible : in a large instrument, it is seen that the surface
is principally made up of luminous masses— described by
Sir William Herschel as corrugations. The luminous
masses present to different observers almost every variety
of irregular form : they have been stated to resemble
"rice grains," "granules or granulations," and
so on.
116. The word "willow-leaf " very well paints the
appearance of the minute details sometimes observed in
the penumbrae of spots,
which occasionally are made
up apparently of elongated
masses of unequal bright-
ness, so arranged that for
the most part they point
like so many arrows to the
centre of the nucleus, giving
to the penumbra a radiated F*e* 4.— Part of a Sun-spot.
annparanrp Atnthprtim^ " Willow- leaves" detaching them-
ce. At ( es, se|ves from the penumbra. A very
and occasionally in the same faint one at F-
spot, the jagged edge of the penumbra projecting over
the nucleus has caused the interior edge of the penumbra
to be likened to coarse thatching with straw.
117- There are darker or shaded portions between the
granules, often pretty thickly covered with dark dots,
like stippling with a soft lead-pencil ; these are what
have been called "pores" by Sir John Herschel, and
48 ASTRONOMY.
"punc tu lat ions" by his father. Some of these arc
almost black, and are like excessively small eruptive spots.
118. When the Sun is totally eclipsed,— that is, as
will be explained by and by, when the Moon comes exactly
between the Earth and the Sun, — other appsarances are
unfolded to us, which the extreme brightness of the Sun
prevents our observing under ordinary circumstances :
the Sun's atmosphere is seen to contain red masses of fan-
tastic shapes, some of them quite disconnected from the
Sun ; to these the names of " red-flames " and " promi-
nences " have been given. Now, as these bodies appear
much brighter than the surrounding atmosphere, we con-
clude that they are hotter than the atmosphere, as a bright
fire is hotter than a dim one.
LESSON IX. — EXPLANATION OF THE APPEARANCES ON
THE SUN'S SURFACE. THE SUN'S LIGHT AND HEAT.
SUN-FORCE. THE PAST AND FUTURE OF THE SUN.
119. We are now familiar with the appearances presented
to us on the Sun's surface in a powerful telescope. Let us
see if we can account for them. As the spots break out
and close up with great rapidity, as changes both on the
large and small scale are always going on on the surface,
we can only infer that the photosphere of the Sun, and
therefore of the stars, is of a cloudy nature ; but while
our clouds are made up of particles of water, the clouds
on the Sun must be composed of particles of various metals
and other substances in a state of intense heat — how hot
we shall see by and by. The photosphere is surrounded
by an atmosphere composed of the vapours of the bodies
which are incandescent in the photosphere. It seems.
THE SUN. 49
also, that not only is the visible surface of the Sun en-
tirely of a cloudy nature, but that the atmosphere is a
highly-absorptive one. Thus when the clouds are
highest they appear brightest — we see facula — because
they extend high into that atmosphere, and consequently
there is less atmosphere to obscure our view there than
elsewhere. Spots may be due either to the absorption of
a greater thickness of atmosphere, as they are hollows
in the cloudy surface, or to the whole of the cloudy
surface being cleared off in those parts from a something
which emits less light than the clouds. The more minute
features — the granules — are most probably the dome-like
tops of the smaller masses of the clouds, bright for the
same reason that the faculae are bright, but to a less
degree ; and the fact that these granules lengthen out as
they approach a spot and descend the slope of the pen-
umbra, may possibly be accounted for by supposing them
to be elongated by the current which causes their down-
rush into a spot, as the clouds in our own sky are
lengthened out when they are drawn into a current.
120. Some spots cover millions of square miles, and
remain for months ; others are only visible in powerful
instruments, and aie of very short duration. There is a
great difference in the number of spots visible from time to
time ; indeed, there is a minimum period, when none
are seen for weeks together, and a maximum period,
when more are seen than at any other time. The interval
between two maximum periods, or two minimum periods,
is about eleven years.
121. Now as we must get less light from the Sun when
he is covered with spots than when there are none, we may
look upon him as a variable star, with a period of
eleven years. Mr. Balfour Stewart has shown recently
that this period is in some way connected with the action of
the planets on the photosphere. It is also known that the
E
50 ASTRONOMY.
magnetic needle has a period of the same length, its
greatest oscillations occurring when there are most sun-
spots. Auroras, and the currents of electricity which
traverse the Earth's surface, are affected by a similar
period.
122. Of the theories by which various astronomers have
attempted to account for sun-spots we shall in this little
book say nothing, as recent discoveries have shown that
the old ones must be reconsidered, and those lately put
forward are not yet sufficiently established.
123. We have before seen (Art. 67) what substances
exist in a state of incandescence in some of the stars. In
the case of the Sun we are acquainted with a greater
number. Here is the list :—
Elements in the Sun.
Sodium. Zinc. Gold, probable.
Iron. Calcium. Cobalt, doubtful.
Magnesium. Chromium. Strontium, ditto.
Barium. Nickel. Cadmium, ditto.
Copper. Hydrogen, probable. Potassium, ditto.
The atmosphere of the Sun, like the atmosphere of the
stars, consists of the vapours of these and of other — yet
unknown — substances, and extends to a height exceeding
80,000 miles above the visible surface.
124. Now let us inquire into some of the benign in-
fluences spread broadcast by the Sun. We all know that
our Earth is lit up by its beams, and that we are warmed
by its heat ; but this by no means exhausts its benefits,
which we share in common with the other planets which
gather round its hearth.
125. And first, as to its light. We have already com-
pared its light with that which we receive from the stars,
but that is merely its relative brightness; we want
THE SUN. 51
now to know its actual, or, as it is otherwise called, its
intrinsic brightness. Now it is clear, at once, that
no number of candles can rival this brightness ; let us
therefore compare it with one of the brightest lights that
we know of — the lime-light. The lime-light proceeds from
a ball of lime made intensely hot by a flame composed
of a mixture of hydrogen and oxygen playing on it. It
is so bright, that we cannot look on it any more than we
can look on the Sun ; but if we place it in front of the
Sun, and look at both through a dark glass, the lime-
light, though so intensely bright, looks like a black
spot. In fact, Sir John Herschel has found that the
Sun gives out as much light as 146 lime-lights
would do if each ball of lime were as large as
the Sun and gave out light from all parts of
its surface.
126. Then, as to the Sun's heat. The heat thrown
out from every square yard of the Sun's surface
is as great as that which would be produced by
burning six tons of coal on it each hour. Now,
we may take the surface of the Sun roughly at
2,284,000,000,000 square miles, and there are 3,097,600
square yards in each square mile. How many tons of
coal must be burnt, therefore, in an hour, to represent
the Sun's heat ?
127. But the Sun sends out, or radiates, its light and
heat in all directions; it is clear, therefore, that as our
Earth is so small compared with the Sun, and is so far
away from it, the light and heat the Earth can inter-
cept is but a very small portion of the whole amount ;
in fact, we only grasp the ^2TSTfW{F7itn Part of it. That
is to say, if we suppose the Sun's light and heat
to be divided into two hundred and twenty-
seven million parts, we only receive one of
them.
E 2
52 ASTRONOMY.
128. But this is not all. There is something else be-
sides light and heat in the Sun's rays, and to this some-
thing we owe the fact that the Earth is clad with verdure ;
that in the tropics, where the Sun shines always in its
might, vegetable life is most luxuriant, and that with us the
spring time, when the Sun regains its power, is marked by
a new birth of flowers. There comes from the Sun, besides
its light and heat, another force, chemical force, which
separates carbon from oxygen, and turns the gas which,
were it to accumulate, would kill all men and animals,
into the life of plants. Thus, then, does the Sun
build up the vegetable world.
129. Now, let us think a little. The enormous engines
which do the heavy work of the world ; the locomotives
which take us so smoothly and rapidly across a whole
continent; the mail-packets which take us so safely across
the broad ocean ; owe all their power to steam, and steam
is produced by heating water by coal. We all know that
coal is the remains of an ancient vegetation ; we have just
seen that vegetation is the direct effect of the Sun's action.
Hence, without the Sun's action in former times we should
have had no coal. The heavy work of the world,
therefore, is indirectly done by the Sun.
130. Now for the light work. Let us take man. To
work a man must eat. Does he eat beef? On what was
the animal which supplied the beef fed ? On grass. Does
he eat bread ? What is bread ? Corn. In both these,
and in all cases, we come back to vegetation, which is, as
we have already seen, the direct effect of the Sun's action.
Here again, then, we must confess that to the Sun is due
man's power of work. All the world's work, therefore,
with one trifling exception (tide-work, of which more
presently), is done by the Sun, and man himself, prince
or peasant, is but a little engine, which directs merely
the energy supplied by the Sun.
THE SUN. 53
131. Will the Sun, then, keep up for ever a supply of
this force? It cannot, if it be not replenished, any more
than a fire can be kept in unless we put on fuel; any more
than a man can work without food. At present, philoso-
phers are ignorant of any means by which it is replenished.
As, probably, there was a time when the Sun existed
as matter diffused through infinite space, the coming
together of which matter has stored up its heat, so,
probably, there will come a time when the Sun, with all
its planets welded into its mass, will roll, a cold, black
ball, through infinite space.*
132. Such, then, is our Sun — the nearest star.-
Although some of the stars do not contain those elements
which on the earth are most abundant — a Orionis and (3
Pegasi, for instance, are worlds without hydrogen — still
we see that, on the whole, the stars differ from each other,
and from our Sun, only by the lower order of differences
of special modification, and not by the more important
differences of distinct plans of structure. There is, there-
fore, a probability that they fulfil an analogous purpose ;
and are, like our Sun, surrounded with planets, which by
their attraction they uphold, and by their radiation illu-
minate and energize. As has been previously pointed
out, the elements most widely diffused through the host
of stars are some of those most closely connected with
the constitution of the living organisms of our globe,
including hydrogen, sodium, magnesium, and iron.
The probable past and future of the Sun are, therefore,
the probable past and future of every star in the firmament
of heaven.
* Sir W. Thomson
CHAPTER HI.
THE SOLAR SYSTEM.
LESSON X.— GENERAL DESCRIPTION. DISTANCES OF
THE PLANETS FROM THE SUN. SIZES OF THE
PLANETS. THE SATELLITES. VOLUME, MASS, AND
DENSITY OF THE PLANETS.
133. From the Sun we now pass to the system of bodies
which revolve round it; and here1, as elsewhere in the
heavens, we come upon the greatest variety. We find
planets — of which the Earth is one — differing greatly in
size, and situated at various distances from the Sun. We
find again a ring of little planets clustering in one part of
the system ; these are called asteroids, or minor planets :
and we already know of at least two masses or rings of
smaller planets still, some of them so small that they
weigh but a few grains : these give rise to the appear-
ances called meteors, bolides, or shooting-stars. We
find also comets, some of which break in, as it were,
upon us from all parts of space ; and then, passing round
our Sun, rush back again : we find others so little erratic
that they may be looked upon as members of the solar
household. Besides these there is another ring which
is rendered visible to us by the appearance called the
Zodiacal Light.
THE SOLAR SYSTEM. 55
134-. The Solar System, then, consists of the follow-
ing:—
Eight large Planets, as follow, in the order of distance
from the Sun :—
1. Mercury. 5. Jupiter.
2. Venus. 6. Saturn.
3. EARTH. 7. Uranus.
4. Mars. 8. Neptune.
Ninety-seven small Planets revolving round the Sun
Between the orbits of Mars and Jupiter. Their names
are given in the Appendix.
Meteoric bodies, which at times approach near the
larth's orbit, and occasionally reach the Earth's surface.
Comets.
The Zodiacal Light. A ring of apparently nebu-
lous matter, the exact nature and position oi
which in the system are not yet determined.
135. Let us begin by getting some general notions of
this system. In the first place, all the planets travel
round the Sun in the same direction, and that
direction, looking down upon the system from the northern
side of it, is from west to east, or, in other words, in
the opposite direction to that in which the hands of a
clock or a watch move. Secondly, the forms of the
paths of all the planets and of many of the
comets are elliptical, but some are very much more
elliptical than others.
136. Next let the reader turn back to Article 105, in
which we have attempted to give an idea of the plane
of the Ecliptic. Now, the larger planets keep very
nearly to this level, which is represented in the following
figure.
ASTRONOMY.
Fig. 5. — Section, or side view, of the plane of the Ecliptic, showing that the
orbits of the large planets are nearly in the plane ; that the orbit of Pallas
has the greatest dip or inclination to it ; and that the orbits of the comets
are inclined to it in all directions.
The straight line we suppose to represent the Earth's orbit
looked at edgeways, as we can look at a hoop edgeways.
The others represent the orbits of some of the planets
and of some of the comets seen edgeways in the same
manner. The orbits of Mars, Jupiter, Saturn, Uranus, and
Neptune lie so nearly in the plane of the ecliptic, that
in our figure, the scale of which is very small, they
may be supposed to lie in that plane. With some of
the smaller planets and comets we see the case is very
different. The latter especially plunge as it were down
into the surface of our ideal sea, or plane of the
ecliptic, in all directions, instead of floating on, or
revolving in it.
137. Again, as we thus find planets travelling round
the Sun, so also do we find other bodies travelling round
some of the planets. These bodies are called Moons,
or Satellites; The Earth, we know, has one Moon ;
Jupiter has four, Saturn eight, Uranus four, and Neptune,
according to our present knowledge, one.
138. As we have before stated, all the planets revolve
round the Sun in one direction, i.e. from west to east.
All the planets rotate, or turn on their axes, in the same
THE SOLAR SYSTEM. 57
direction, and so do the satellites, with one exception.
This exception is found in the motion of the satellites of
the planet Uranus, which move from east to west.
139. Let us next inquire into the various distances
of the planets from the Sun, bearing in mind, that as the
orbits are elliptical, the planets are sometimes nearer
to the Sun than at other times. This will be explained
by and by ; in the meantime we may say, that the average
or mean distances are as follow; the times of revo-
lution are also given : —
Period of revolution round
Distance in Miles. the Sun.
D. H. M.
Mercury. . . . 35,393,o°o • • 87 23 15
Venus .... 66,130,000 . . 224 16 48
EARTH. . . . 91,430,000 . . 365 6 9
Mars .... 139,312,000 . . 686 23 31
Jupiter .... 475,693,000 . . 4332 14 2
Saturn .... 872,135,000 . . 10759 5 16
Uranus . . . 1,752,851,000 . . 30686 17 21
Neptune . . .2,746,271,000 . . 60118 o o
140. Let us next see what are the sizes of the different
planets. Their diameters are as follow : —
Diameter in Miles.
Mercury 2,962
Venus 7>5io
EARTH 7,901
Mars 4,000
Jupiter . . 85,390
Saturn 7i?9O4
Uranus 33,024
Neptune 36,620
141. We have before attempted to give an idea of the
comparative sizes of the Earth and Sun, and of the dis-
tance between them ; let us now complete the picture. Still
5B ASTRONOMY.
taking a globe some two feet in diameter to represent the
Sun, Mercury would now be proportionately represented
by a grain of mustard-seed, revolving in a circle 164 feet
in diameter ; Venus, a pea, in a circle of 284 feet in
diameter ; the Earth also a pea, at a distance of 430 feet ;
Mars, a rather large pin's head, in a circle of 654 feet ;
the smaller planets by grains of sand, in orbits of from
1,000 to 1,200 feet; Jupiter, a moderate sized orange, in
a circle nearly half a mile across ; Saturn, a small orange,
in a circle of four-fifths of a mile ; Uranus, a full-sized
cherry, or small plum, upon the circumference of a circle
more than a mile and a half; and Neptune, a good-
sized plum, in a circle about two miles and a half in
diameter.*
14-2. As the planets revolve round the Sun at vastly dif-
ferent distances, so do the satellites revolve round their
primaries. Our solitary Moon courses round the Earth at
a distance of 240,000 miles, and its journey is performed
in a month. The first satellite of the planet Saturn is
only about one-third of this distance, and its journey is
performed in less than a day. The first satellite of
Uranus is about equally near, and requires about two and
a half days. The first satellite of Jupiter is about the
same distance from that planet as our Moon is from us,
and its revolution is accomplished in one and three-
quarters of our days. The only satellite which takes a
longer time to revolve round its primary than our Moon,
is Japetus, the eighth satellite of Saturn. We have seen
above (Art. 140), that the diameter of the smallest planet
— leaving the asteroids out of the question — is 2,962 miles.
We find that among the satellites we have three bodies —
the third and fourth satellites of Jupiter, and the sixth
moon of Saturn — of greater dimensions than one of the
* Sir John Herschel.
THE SOLAR SYSTEM. 59
large planets, Mercury, and nearly as large as another,
Mars.
It is not necessary in this place to give more details
concerning the distances and sizes of the planets and
satellites. A complete statement will be found in Tables
II. and III. of the Appendix.
14-3- The relative distances of the planets from
the Sun was known long before their absolute dis-
tances— in the same way as we might know that one
place was twice or three times as far away as another
without knowing the exact distance of either. When once
the distance of the Earth from the Sun was known, astro-
nomers could easily find the distance of all the rest from
the Sun, and therefore from the Earth. Their sizes were
next determined, for we need only to know the distance
of a body and its apparent size, or the angle under which
we see it, to determine its real dimensions.
14-4-. In the case of a planet accompanied by satellites
we can at once determine its weight, or mass, for a
reason we shall state by and by (Chap. IX.); and when we
have got its weight, having already obtained its size or
volume, we can compare the density of the materials of
which the planet is composed with those we are familiar
with here ; having first also obtained experimentally the
density of our own Earth.
14-5. Let us see what this word density means. To
do this, let us compare platinum, the heaviest metal, with
hydrogen, the lightest gas. The gas is, to speak roughly,
a quarter of a million times lighter than the metal ; the
gas is therefore the same number of times less dense :
and if we had two planets of exactly the same size, one
composed of platinum and the other of hydrogen, the
latter would be a quarter of a million times less dense
than the former. Now, if it seems absurd to talk of a
hydrogen planet, we must remember that if the materials
60 ASTRONOMY.
of which our system, including the Sun, is composed,
once existed as a great nebulous mass extending far be-
yond the orbit of Neptune, as there is reason to believe,
the mass must have been more than 200,000,000 times
less dense than hydrogen !
146. Philosophers have found that the mean density of
the Earth is a little more than five and a half times that
of water, that is to say, our Earth is five and a half times
heavier than it would be if it were made up of water. If
we now compare the density of the other planets with it,
we find that they almost regularly increase in density as
we approach the Sun ; Mercury being the most dense ;
Venus, the Earth, and Mars, having densities nearly alike,
but less than that of Mercury; while Saturn and Uranus
are the least dense.
147. Here is a Table showing the volumes, masses,
and densities of the planets ; those of the Earth being
taken as 100 : —
Volume or Mass-or -n^r,*:*™
Size. Weight. Density.
Mercury . . 5 . 7 ... 124
Venus .... 80 . 79 ... 90
EARTH ... 100 . 100 . . . 100
Mars ... 14 . 12 ... 96
Jupiter . . . 138,700 . 30,000 ... 20
Saturn . . . 74,600 . 9,000 ... 12
Uranus . . . 7,200 . 1,300 ... 18
Neptune . . 9,400 . 1,700 ... 17
148. To sum up, then, our first general survey of the
Solar System, we find it composed of planets, satellites,
comets, and several rings or masses of meteoric bodies ;
the planets, both large and small, revolving round the
Sun in the same direction, the satellites revolving in a
similar manner round the planets. We have learned the
mean distances of the planets from the Sun, and we have
THE SOLAR SYSTEM. 61
compared the distances and times of revolution of some
of the satellites. We have also seen that the volumes,
masses, and densities of the various planets have been
determined. There is still much more to be learnt, both
about the system generally, and the planets particularly;
but it will be best, before we proceed with our general
examination, to inquire somewhat minutely into the move-
ments and structure of the Earth on which we dwell.
LESSON XI. — THE EARTH. ITS SHAPE. POLES.
EQUATOR. LATITUDE AND LONGITUDE. DIAMETER.
149. As we took the Sun as a specimen of the stars,
because it was the nearest star to us, and we could there-
fore study it best, so now let us take our Earth, with
which we should be familiar, as a specimen of the planets.
150. In the first place, we have learned that it is
round. Had we no proof, we might have guessed this,
because both Sun and Moon, and the planets observable
in our telescopes, are round. But we have proof. The
Moon, when eclipsed, enters the shadow thrown by the
Earth ; and it is easy to see on such occasions, when the
edge of the shadow is thrown on the bright Moon, that
the shadow is circular.
151. Moreover, if we watch the ships putting out to
sea, we lose first the hull, then the lower sails, until at
last the highest parts of the masts disappear. Similarly
the sailor, when he sights land, first catches the tops of
mountains, or other high objects, before he sees the beach
or port. If the surface of the Earth were an extended
plain, this would not happen ; we should see the nearest
things and the biggest things best : but as it is, every point
62 ASTRONOMY.
of the Earth's surface is the top, as it were, of a flattened
dome ; such a dome therefore is interposed between us
and every distant object. The inequalities of the land
render this fact much less obvious on terra firma than on
the surface of the sea.
152. On all sides of us we see a circle of land, or sea,
or both, on which the sky seems to rest : this is called the
sensible horizon. If we observe it from a little boat on
the sea, or on a plain, this circle is small ; but if we look
out from the top of a ship's mast or from a hill, we find
it largely increased — in fact, the higher we go the more is
the horizon extended, always however retaining its circular
form. Now, the sphere is the only figure which, looked
at from any external point, is bounded by a circle; and
as the horizons of all places are circular, the Earth is a
sphere, or at all events nearly so.
153- The Earth is not only round, but it rotates,
or turns round on an axis, as a top does when it is
spinning ; and the names of north pole and south pole
are given to those points on the Earth where the axis
would come to the surface if it were a great iron rod
instead of a mathematical line. Half-way between these
two poles, there is an imaginary line running round the
Earth, called the equator or equinoctial line- The
line through the Earth's centre from pole to pole is
called the polar diameter; the line through the Earth's
centre from any point in the equator to the opposite
point is called the equatorial diameter, and one of these,
as we shall see, is longer than the other.
154. We owe to the ingenuity of a French philosopher,
M. Le*on Foucault, two experiments which render the
Earth's rotation visible to the eye. For although, as we
shall presently see, it is made evident by the apparent
motion of the heavenly bodies and the consequent suc-
cession of day and night, we must not forget that these
THE SOLAR SYSTEM. 63
effects might be, and for long ages were thought to be,
produced by a real motion of the Sun and stars round
the Earth. The first method consists in allowing a heavy
weight, suspended by a fine wire, to swing backwards and
forwards like the pendulum of a clock. Now, if we move
the beam or other object to which such a pendulum is
suspended, we shall not alter the direction in which the
pendulum swings, as it is more easy for the thread or
wire, which supports the weight, to twist than for the
heavy weight itself to alter its course or swing when once
in motion in any particular direction. Therefore, in the
experiment, if the earth were at rest, the swing of the
pendulum would always be in the same direction with
regard to the support and the surrounding objects.
155. M. Foucault's pendulum was suspended from the
dome of the Panthdon in Paris, and a fine point at the
bottom of the weight was made to leave a mark in sand
at each swing. The marks successively made in the sand
showed that the plane of oscillation varied with regard to
the building. Here, then, was a proof that the building,
and therefore the Earth, moved.
156. Such a pendulum swinging at either pole would
make a complete revolution in 24 hours, and would serve
the purpose of a clock were a dial placed below it with
the hours marked. As the Earth rotates at the north pole
from west to east, the dial would appear to a spectator,
carried like it round by the Earth, to move under the
pendulum from west to east, while at the south pole the
Earth and dial would travel from east to west : midway
between the poles, that is, at the equator, this effect, of
course, is not noticed, as there the two motions in
opposite directions meet.
157- The second method is based upon the fact, that
when a body turns on a perfectly true and symmetrical
axis, and is left to. itself in such a manner that gravity is
64 ASTRONOMY.
not brought into play, the axis maintains an invariable
position ; so that if it be made to point to a star, which is
a thing outside the Earth and not supposed to move, it
will continue to point to it. A gyroscope is an instrument
so made that a heavy wheel set into very rapid motion
shall be able to rotate for a long period, and that all
disturbing influences, the action of gravity among them,
are prevented.
158. Now, if the Earth were at rest, there would be no
apparent change in the position of the axis, however long
the wheel might continue to turn ; but if the Earth moves
and the axis remain at rest, there should be some differ-
ence. Experiment proves that there is a difference, and
just such a difference as is accounted for by the Earth's
rotation. In fact, if we so arrange the gyroscope that the
axis of its rotation points to a star, it will remain at rest
with regard to the star, while it varies with regard to the
Earth. This is proof positive that it is the Earth which
rotates on its axis, and not the stars which revolve round
it ; for if this were the case the axis of the gyroscope
would remain invariable with regard to the Earth, and
change its direction with regard to the star.
159. If we look at a terrestrial globe, we find that the
equator is not the only line marked upon it. There are
other lines parallel to the equator, — that is, lines which are
the same distance from the equator all round, — and other
lines passing through both poles, and dividing the equator
into so many equal parts. These lines are for the purpose
of determining the exact position of a place upon the
globe, and they are based upon the fact, that all circles
are divided into 360 degrees (marked °), each degree into
60 minutes ('), and each minute into 60 seconds (").
160. We have first the equator midway between the
poles, so that from any part of the equator to either pole
is one quarter round the P^arth, or 90 degrees. On either
THE SOLAR SYSTEM. 6$
side of the equator there are circles parallel to it ; that is
to say, at the same distance from it all round, dividing the
distance to the poles into equal parts. Now, it is necessary
to give this distance from the equator some name. The
term latitude has been chosen. North latitude from
the equator towards the north pole ; south latitude
from the equator towards the south pole.
161. This, however, is not sufficient to define the exact
position of a place, it only defines the distance from the
equator. This difficulty has been got over by fixing upon
Greenwich, our principal astronomical observatory, and
supposing a circle passing through the two poles and that
place, and then reckoning east and west from the circle
as we reckon north and south from the equator. To this
east and west reckoning the term longitude has been
applied.
162. On the terrestrial Globe we find what are termed
parallels of latitude, and meridians of longitude, at every
10° or 15°. Besides these, at 23 y on either side of the
equator, are the Tropics : the north one the tropic of
Cancer, the southern one the tropic of Capricorn; and
at the same distance from either pole, we find the arctic
and antarctic circles. These lines divide the Earth's
surface into five zones — one torrid, two temperate, and
two frigid zones.
163. The distance along the axis of rotation, from pole
to pole, through the Earth's centre, is shorter than the
distance through the Earth's centre from any one point
in the equator to the opposite one. In other words, the
diameter from pole to pole (the polar diameter) is shorter
than the one in the plane of the equator (the equatorial
diameter), and their lengths are as follow : —
Feet.
Polar diameter .... 41,848,380
Equatorial diameter . . 41,708,710
F
66 ASTRONOMY.
Now turn these feet into miles : the difference after all is
small; but still it proves that the Earth is not a sphere,
it is what is called an oblate spheroid.
LESSON XII.— THE EARTH'S MOVEMENTS. ROTATION.
MOVEMENT ROUND THE SUN. SUCCESSION OF DAY
AND NIGHT.
1 64. The Earth turns on its axis, or polar diameter,
in 23 h. 56m. In this time we get the succession of day
and night, which succession is due therefore to the
Earth's rotation. Before we discuss this further we must
return to another of the Earth's movements. We know
also that it goes round the Sun, and the time in which
that revolution is effected we call a year.
165. Let us now inquire into this movement round the
Sun. We stated (Art. 135) that the planets travelled round
the centre of the system in ellipses. We will here state
the meaning of this. If the orbits were circular, the
planet would always be the same distance from the Sun,
as all the diameters of a circle are equal ; but an ellipse
is a kind of flattened circle, and some parts of it are nearer
the centre than others.
166. In Fig. 6 the outermost ring is a circle, which can
be' easily constructed with a pair of compasses, or by
sticking a pin into paper, throwing a loop over it, keeping
the loop tight by means of a pencil, and letting the pencil
travel round. The two inner rings are ellipses. It is seen at
once that one is very like the circle, and the other unlike it.
The points D E and F G are called the foci of the two
ellipses, and the shape of the ellipse depends upon the
distance these points are apart. We can see this for
THE SOLAR SYSTEM. 67
ourselves if we stick two pins in a piece of paper, pass a
loop of cotton over them, tighten the cotton by means
of a pencil, and, still keeping the cotton tight, let the
pencil mark the paper, as in the case of the circle. The
6. — Showing the difference between a circle and ellipses of different
eccentricities, and how they are constructed.
pencil will draw an ellipse, the shape of which we may
vary at pleasure (using the same loop) by altering the
distance between the/oct.
167. Now the Sun does not occupy the centre of the
ellipse described by the Earth, but one of the foci. It
results from this, that the Earth is nearer the Sun at one
time than another. When these two bodies are nearest
F 2
68
ASTRONOMY.
together, we say the Earth is in perihelion.* When they
are furthest apart, we say it is in aphelion, f Let us now
make a sketch of the orbit of the Earth as we should see
it if we could get a bird's-eye view of it, and determine the
points the Earth occupies at different times of the year,
and how it is presented to the Sun.
Fig. 7. — The Earth's path round the Sun.
168. Now refer back to Art. 106, in which we spoke of
the position of the Sun's axis. We found that the Sun was
not floating uprightly in our sea, the plane of the ecliptic :
* wept, at or near to ; rjXiov, the Sun.
f OTTO, from, and »,Aio?.
THE SOLAR SYSTEM. 69
it was dipped down in a particular direction. So it is
with our Earth. The Earth's axis is inclined in the same
manner, but to a much greater extent. The direction of
the inclination, as in the case of the Sun, is, roughly
speaking, always the same.
169. We have then two completely distinct motions —
one round the axis of rotation, which, roughly speaking,
remains parallel to itself, performed in a day; — one
round the Sun, performed in a year. To the former
motion we owe the succession of day and night; to the
latter, combined with the inclination of the Earth's axis,
we owe the seasons.
170. In Fig. 7 is given a bird's-eye view of the system.
It shows the orbit of the Earth, and how the axis of the
Earth is inclined — the direction of the dip being such
that on the 2ist of June the axis is directed towards the
Sun, the inclination being 23 J°. Now, if we bear in mind
that the Earth is spinning round once in twenty-four
hours, we shall immediately see how it is we get day and
night. The Sun can only light up that half of
the Earth turned towards it; consequently, at any
moment, one-half of our planet is in sunshine, the other
in shade ; the rotation of the Earth bringing each part in
succession from sunshine to shade.
171. But it will be asked, " How is it that the days and
nights are not always equal ?" For a simple reason. In
the first place, the days and nights are equal all over the
world on the 22d of March and the 22d of September,
which dates are called the vernal and autumnal equinoxes
for that very reason— equinox being the Latin for equal
night. But to make this clearer, let us look at the small
circle we have marked on the Earth — it is the arctic circle.
Now let us suppose ourselves living in Greenland, just
within that circle. What will happen ? At the spring
equinox (it will be most convenient to follow the order of
70 ASTRONOMY.
the year) we find that circle half in light and half in shade.
One-half of the twenty-four hours (the time of one rotation),
therefore, will be spent in sunshine, the other in shade :
in other words, the day and night will be equal, as we
before stated. Gradually, however, as we approach the
summer solstice (going from left to right), we find the
circle coming more and more into the light, in consequence
of the inclination of the axis, until, when we arrive at the
solstice, in spite of the Earth's rotation, we cannot get oui
of the light. At this time we see the midnight sun due
north ! The Sun, in fact, does not set. The solstice
passed, we approach the autumnal equinox, when again
we shall find the day and night equal, as we did at the
vernal equinox. But when we come to the winter solstice,
we get no more midnight suns : as shown in the figure,
all the circle is situated in the shaded portion ; hence,
again in spite of the Earth's rotation, we cannot get oitt
of the darkness, and we do not see the Sun even at
noonday.
172. Now, these facts must be well thought of. If this
be done there will be no difficulty in understanding how
it is that at the poles (both north and south) the years
consist of one day of six months' duration, and
one night of equal length. To comprehend our
long summer days and short nights in England, we have
only to take a part about half-way between the arctic
circle and the equator, as marked on the plate, and reason
in the same way as we did for Greenland. At the equator
we shall find the day and night always equal.
173. Here is a Table showing the length of the
longest days in different latitudes, from the equator to the
poles. We see that the Earth's surface on either side the
equator may be divided into two zones, in one of which the
days and nights are measured by hours, and in the other
by months : —
THE SOLAR SYSTEM.
o
O
16
4i
61
63
64
o (Equator)
Hours.
12
0
48 .
Hours.
. . 22
AA
66
21 ....
4.8
66
24.
24. .
I c
2
16
67
27
Month.,.
j
17
**/
60
27
. . 18
vy
4.O
•»
IQ .
IQ
78
II..*.
4.
2O
81
c
SO .
21
QO
o (Pole)
6
What we have said about the northern hemisphere
applies equally to the southern one, but the diagram will
not hold good, as the northern winter is the southern
summer, and so on ; and moreover, if we could look upon
our Earth's orbit from the other side, the direction of the
motions would be reversed. The reader should construct
a diagram for the southern hemisphere for himself.
LESSON XIII. — THE SEASONS.
175. So much, then, for the succession of day and
night. The seasons next demand our attention. Now,
the changes to which we inhabitants of the temperate
zones are accustomed, the heat of summer, the cold of
winter, the medium temperatures of spring and autumn,
depend simply upon the height to which the Sun attains
at mid-day. The proof of this lies in the facts that on the
equator the Sun is never far from the zenith, and we have
perpetual summer : near the poles, — that is, in the frigid
zones, — the Sun never gets very high, and we have per-
72 ASTRONOMY.
petual winter. How, then, are the changing seasons in
the temperate zones caused ?
176. In Fig. 7 we were supposed to be looking down
upon our system. We will now take a section from
solstice to solstice through the Sun, in order that we may
have a side view of it. Here, then, in Fig. 8, we have
the Earth in two positions, and the Sun in the middle.
Fig. 8. — Explanation of the apparent altitude. of the Sun, as seen from
London, in Summer and Winter.
On the left we have the winter solstice, where the axis of
rotation is inclined away from the Sun to the greatest
possible extent. On the right we have the summer sol-
stice, when the axis of rotation is inclined towards the
Sun to the greatest possible extent. The line ab in
both represents the parallel of latitude passing through
London. The dotted line from the centre through b
shows the direction of the zenith — the direction in which
our body points when we stand upright. We see that
this line forms a larger angle with the line leading to
the Sun, or the two lines open out wider, at the winter
solstice, than they do at the summer one. Hence we see
the Sun in winter at noon, low down, far from the zenith,
while in summer we are glad to seek protection from his
beams nearly overhead. Tlie reader should now make a
THE SOLAR SYSTEM.
73
similar diagram to represent the position of the Sun at
the equinoxes ; he will find that the axis is not then in-
clined either to or from the Sun, but sideways, the result
being that the Sun itself is seen at the same distance from
the point overhead in spring and autumn, and hence
the temperature is nearly the same, though Nature ap-
parently works very differently at these two seasons ; in
one we have the sowing-time, in the other the fall of the
leaf.
Fig. 9. — The Earth, as seen from the Sun at the Summer Solstice
(noon at London).
177. Perhaps the Sun's action on the Earth, in giving
rise to the seasons, will be rendered more clear by in-
quiring how the Earth is presented to the Sun at the four
seasons — that is, how the Earth would be seen by an
74 ASTRONOMY.
observer situated in the Sun. First, then, for summer
and winter. Figs. 9 and 10 represent the Earth as it would
be seen from the Sun at noon in London, at the summer
and winter solstices. In the former, England is seen well
down towards the centre of the disc, where the Sun is
vertical, or overhead ; its rays are therefore most felt, and
we enjoy our summer. In the latter, England is so near
Fig. 10. — The Earth, as seen from the Sun at the Winter Solstice
(noon at London).
the northern edge of the disc that it cannot be properly
represented in the figure. It is therefore furthest from
the region where the Sun is overhead ; the Sun's rays are
consequently feeble, and we have winter.
178. In Figs. II and 12, representing the Earth at the
two equinoxes, we see that the position of England, with
THE SOLAR SYSTEM. 75
regard to the centre of the disc, is the same— the only
difference being that in the two figures the Earth's axis is
inclined in different directions. Hence there is no differ-
ence in temperature at these periods.
179. These figures should be well studied in connexion
with Fig. 7, and also with Art. 170, in which the cause of
the succession of day and night is explained. All these
Fig. ii. — The Earth, as seen from the Sun at the Vernal Kquii.ox
(noon at London).
drawings represent London on the meridian which passes
through the centre of the illuminated side of the Earth. It
must therefore be noon at that place, as noon is half-way
between sunrise and sunset. All the places represented on
the western border have the Sun rising upon them ; all the
places on the eastern border have the Sun setting. As,
76 ASTRONOMY.
therefore, at the same moment of absolute time we have
the Sun rising at some places, overhead at others, and
setting at others, we cannot have the same time, as
measured by the Sun, at all places alike.
Fig. 12. — The Earth, as seen from the Sun at the Autumnal Equinox
(noon at London).
18O. In fact, as the Earth, whose circumference is
divided into 360° (Art. 159), turns round once in twenty-
four hours, the Sun appears to travel 15° in one hour from
east to west. One degree of longitude, therefore,
makes a difference of four minutes of time, and
vice versd.
THE SOLAR SYSTEM. 77
LESSON XIV.— STRUCTURE OF THE EARTH. THE
EARTH'S CRUST. INTERIOR HEAT OF THE EARTH.
CAUSE OF ITS POLAR COMPRESSION. THE EARTH
ONCE A STAR.
181. Having said so much of the motions of our Earth
— we shall return to them in a subsequent Lesson — let us
now turn to its structure, or physical constitution.
We all of us are acquainted with the present appear-
ance of our globe, how that its surface is here land,
there water ; and that the land is, for the most part,
covered with soil which permits of vegetation, the vege-
tation varying according to the climate ; while in some
places meadows and wood-clad slopes give way to rugged
mountains, which rear their bare or ice-clad peaks to
heaven.
182. Taking the Earth as it is, then, the first question
that arises is, Was it always as it is at present?
The answer given by Geology and Physical Geography,
two of the kindred sciences of Astronomy, is that the
Earth was not always as we now see it, and that for
millions of years changes have been going on, and are
going on still.
183. It has been found, that what is called the Earth's
crust— that is, the outside of the Earth, as the peel is
the outside of an orange — is composed of various rocks
of different kinds and of different ages, all of them how-
ever belonging to two great classes : —
CLASS I. Rocks that have been deposited by water :
these are called stratified or sedimentary
rocks.
CLASS II. Rocks that once were molten : these are
called igneous rocks.
ASTRONOMY.
184. Now, the sedimentary rocks have not always
existed, for when we come to examine them closely it
is found that they are piled one over the other in suc-
cessive layers : the newer rocks reposing upon the older
ones. The order in which these rocks have been deposited
by the sea is as follows :—
List of Stratified Rocks.
Cainozoic, or Tertiary .
•\ f Alluvium.
I Upper ' Drift.
| ( Crag.
Lower
N Upper
Eocene.
Cretaceous.
Mesozoic, or Secondary . I
f Lower -s Lias.
I Trias.
Palaeozoic, or Primary . .
S Permian.
Carboniferous.
N Devonian.
( Silurian.
Lower \ Cambrian.
( Laurentian.
185. That these beds have been deposited by water, and
principally by the sea, is proved by the facts — first, that
in their formation they resemble the beds being deposited
by water at the present time ; and, secondly, that they
nearly all contain the remains of fishes, reptiles, and
shell-fish in great abundance — indeed, some of the
beds are composed almost entirely of the remains of
animal life.
186. It must not be supposed that the stratified bed;
THE SOLAR SYSTEM. 79
of which we have spoken are everywhere met with as they
are shown in the Table ; each bed could only have been
deposited on those parts of the Earth's crust which were
under water at the time ; and since the earliest period
of the Earth's history, earthquakes and changes of level
have been at work, as they are at work now — but much
more effectively, either because the changes were more
decided and sudden, or because they were at work over
immense periods of time.
187- It is found, indeed, that the sedimentary rocks
have been upheaved and worn away again, bent, con-
torted, or twisted to an enormous extent ; instead of
being horizontal, as they must have been when they were
originally formed at the bottom of the sea, they are now
seen in some cases upright, in others dome-shaped, over
large areas.
188. Had this not been the case the mineral riches of
the Earth would for ever have been out of our reach, and
the surface of the Earth would have been a monotonous
plain. As it is, although it has been estimated that the
thickness of the series of sedimentary rocks, if found
complete in any one locality, would be 14 miles, each
member of the series is found at the surface at some
place or other.
189. The whole series of the sedimentary rocks, from
the most ancient to the most modern, have been disturbed
by eruptions of volcanic materials, similar to those thrown
up by Vesuvius, and other volcanoes active in our own time,
and intrusions of rocks of igneous origin proceeding from
below ; of which igneous rocks, granite, which in conse-
quence of its great hardness is so largely used for paving
and macadamizing our streets, may here be taken as one
example out of many. These rocks are extremely easy to
distinguish from the stratified ones, as they have no ap-
pearance of stratification, contain no fossils, and their
So ASTRONOMY.
constituents are different, and are irregularly distributed
throughout the mass.
190. If we strip the Earth, then, in imagination, of
the sedimentary rocks, we come to a kernel of rock, the
constituents of which it is impossible to determine, but
which may be imagined to be analogous to the older
rocks of the granitic series, and to have been part of the
original molten sphere which must have been both hot
and luminous, in the same way that molten iron is both
hot and luminous. Doubtless there was a time
when the surface of our earth was as hot and
luminous as the surfaces of the sun and stars
are still.
191. Now, suppose we have a red-hot cannon-ball ;
what happens ? The ball gradually parts with, or radiates
away, its heat, and gets cool, and as it cools it ceases to
give out light ; but its centre remains hot long after the
surface in contact with the air has cooled down.
192. So precisely has it been with our earth ; indeed
we have numerous proofs that the interior of the earth is
at a high temperature at present, although its surface has
cooled down. Our deepest mines are so hot that, without
a perpetual current of cold fresh air, it would be impos-
sible for the miners to live down them. There are hot
springs coming from great depths, and the water which
issues from them is, in some cases, at the boiling tempe-
rature— that is, 100° of the centigrade thermometer. In
the hot lava emitted from volcanoes we have evidence
again of this interior heat, and how it is independent
of that at the surface ; for among the most active
volcanoes with which we are acquainted are Hecla in
Iceland, and Mount Erebus in the midst of the icy deserts
which surround the south pole.
193. It has been calculated that the temperature of
the earth increases as we descend at the rate of J° (cen-
THE SOLAR SYSTEM. 81
tigrade) in about thirty yards. We shall therefore have
a temperature of —
Centigrade. Miles.
1 00° or the temperature of ) , ., r
, .,. fat a depth of . . 2
boiling water . . )
400° or the temperature of ) ,
red-hot iron ... $
i, 000° or the temperature of / g
melted glass ... 1
1,500° or the temperature at^
which everything !
with which we are I
acquainted would [ "
be in a state of i
fusion J
194. If this be so, then the Earth's crust cannot exceed
28 miles in thickness — that is to say, the yi^-th part
of the radius (or of half the diameter), so that it is com-
parable to the shell of an egg. But this question is one
on which there is much difference of opinion, some philo-
sophers holding that the liquid matter is not continuous
to the centre, but that, owing to the great pressure, the
centre itself is solid. Evidence also has recently been
brought forward to show that the Earth may be a solid
or nearly solid globe from surface to centre.
195. The density of the Earth's crust is only about
half of the mean density of the Earth taken as a whole.
This has been accounted for by supposing that the ma-
terials of which it is composed are made denser at great
depths than at the surface, by the enormous pressure of
the overlying mass; but there are strong reasons for
believing that the central portions are made up of much
G
82
ASTRONOMY.
denser bodies, such as metals and their metallic com-
pounds, than are common at the surface.
196. It was prior to the solidification of its crust, and
while the surface was in a soft or fluid condition, that the
Earth put on its present flattened shape, the flattening
being due to a bulging out at the equator, caused by the
Earth's rotation. If we arrange a hoop, as shown in
**£• X3- — Explanation of the Spheroidal form of the Earth.
Fig. 13, and make it revolve very rapidly, we shall see
that that part of the hoop furthest from the fixed points,
and in which the motion is most rapid, bulges out as the
Earth does at the equator.
197. The form of the Earth, moreover, is exactly that
which any fluid mass would take under the same circum-
stances. M. Plateau has proved this by placing a mass of
oil in a transparent liquid exactly of the same density as
the oil. As long as the oil was at rest it took the form
of a perfect sphere floating in the middle of the fluid,
exactly as the Earth floats in space ; but the moment a
slow motion of rotation was given to the oil by means of
a piece of wire forced through it, the spherical form was
changed into a spheroidal one, like that of the Earth.
198. The tales told by geology, the still heated state
of the Earth, and the shape of the Earth itself, all show
that long ago the sphere was intensely heated, and fluid.
THE SOLAR SYSTEM 83
LESSON XV. — THE EARTH (continued). THE ATMO-
SPHERE. BELTS OF WINDS AND CALMS. THE
ACTION OF SOLAR AND TERRESTRIAL RADIATION.
CLOUDS. CHEMISTRY OF THE EARTH. THE EARTH'S
PAST AND FUTURE.
199. Having said so much of the Earth's crust, we must
now, in order to fully consider our Earth as a planet, pass
on to the atmosphere, which may be likened to a great
ocean, covering the Earth to a height which has not yet
been exactly determined. This height is generally sup-
posed to be 45 or 50 miles, but there is evidence to show
that we have an atmosphere of some kind at a height of
400 or 500 miles.
200. The atmosphere, as we know, is the home of the
winds and clouds, and it is with these especially that we
have to do, in order to try to understand the appearances
presented by the atmospheres of other planets. Although
in any one place there seems no order in the production
of winds and clouds, on the Earth treated as a whole
we find the greatest regularity ; and we find, too, that the
Sun's heat and the Earth's rotation are, in the main, the
causes of all atmospheric disturbances.
201. If we examine a map showing the principal move-
ments and conditions of the atmosphere, we shall find,
belting the Earth along the equator, a belt of equatorial
calms and rains. North of this we get a broad region,
a belt of trade-winds, where the winds blow from the
north-east ; to the south we find a similar belt, where the
prevailing winds are south-east. Polewards from these
G 2
84 ASTRONOMY.
belts to the north and south respectively lie the calms of
Cancer and the calms of Capricorn. Still further to-
wards the poles, we find the counter- trades, in regions
where the winds blow from the equator to the poles : i.e.
in the northern hemisphere they blow south and west, and
in the southern hemisphere north and west ; and at the
poles themselves we find a region of polar calms.
202, Now if the Earth did not rotate on its axis we
should still get the trade-winds, but both systems would
blow from the pole to the equator ; but as the Earth does
rotate, the nearer the winds get to the equator the more
rapidly is the Earth's surface whirled round underneath
them ; the Earth, as it were, slips from under them in
an easterly direction, and so the northern trade-winds
appear to come from the north-east, and the southern ones
from the south-east. Similarly, the counter-trades, which
blow towards the poles, appear to come, the northern
ones from the south-west and the southern ones from
the north-west. The nearer they approach the poles the
slower is the motion of the Earth under them, compared
with the regions nearer the equator ; consequently, they
are travelling to the eastward faster than the parallels
at which they successively arrive, and they appear to
come from the westward.
203. Now, how are these winds set in motion ? The
tropics are the part of the Earth which is most heated,
and, as a consequence, the air there has a tendency to
ascend, and a surface-wind sets in towards the equator
on both sides, to fill up the gap, as it were ; when it gets
there it also is heated ; the two streams join and ascend,
and flow as upper-currents towards either pole. Where the
two streams meet in the region of equatorial calms some
4° or 5° broad, we have a cloud-belt, and daily rains. The
counter-trades are the upper-currents referred to above,
which in the regions beyond the calms of Cancer and
THE SOLAR SYSTEM. 85
Capricorn descend to the Earth's surface, and form
surface currents.
2O4-. We see, therefore, that it is the Sun which sets all
this atmospheric machinery in motion, by heating the
equatorial regions of the Earth ; and as the Sun changes
its position with regard to the equator, oscillating up and
down in the course of the year, so do the calm-belts and
trade- winds. The belt of equatorial calms follows the
Sun northwards from January to July, when it reaches
25° N. lat. and then retreats, till at the next January it
is in 25° S. lat.
205. So much for the Sun's direct action, and one of
its effects on our rotating planet — the prevailing wind-
currents, which are set in motion by the ^7iyJ-(nnn> Part
of the Sun's radiation into space, which represents an
amount of heat that would daily raise 7,513 cubic miles
of water from the freezing to the boiling point.
206. To the radiation from the Earth, combined with
the existence of the vapour of water in the air, must be
ascribed all the other atmospheric phenomena. Aqueous
vapour is the great mother of clouds. When it is chilled
by a cold wind or a mountain top, it parts with its heat,
is condensed and forms a cloud; and then mist, rain,
snow, or hail, is formed : when it is heated by the direct
action of the Sun, or by a current of warm air, it absorbs
all the heat and expands, and the clouds disappear.
207. We now come to the materials of which our
planet, including the Earth's crust and atmosphere, is
composed. These are 64 in number ; they are called the
chemical elements. These consist of—
N on- metallic f Nitrogen, oxygen, hydrogen, chlorine,
elements; bromine, iodine, fluorine, silicon,
or boron, carbon, sulphur, selenium,
Metalloids. | tellurium, phosphorus, arsenic.
86 ASTRONOMY.
Metals of the alkalies : — Potassium,
sodium, caesium, rubidium, lithium.
Metallic J Metals of the alkaline earths:— Cal-
eiementa. | cium, strontium, barium.
Other metals: — Aluminium, zinc, iron,
tin, tungsten, lead, silver, gold, £c.
The elements which constitute the great mass of the
Earth's crust are comparatively few — aluminium, calcium,
carbon, chlorine, hydrogen, magnesium, oxygen, potas-
sium, silicon, sodium, sulphur. Oxygen combines with
many of these elements, and especially with the earthy
and alkaline metals ; indeed, one-half of the ponderable
matter of the exterior parts of the globe is composed
of oxygen in a state of combination. Thus sandstone,
the most common sedimentary rock, is composed of silica,
which is a compound of silicon and oxygen, and is half
made up of the latter ; granite, a common igneous rock,
composed of quartz, felspar, and mica, is nearly half
made up of oxygen in a state of combination in those
substances.
2O8. The chemical composition, by weight, of 100
parts of the atmosphere at present is as follows :—
Nitrogen .... 77 parts.
Oxygen 23 „
Besides these two main constituents, we have —
Carbonic acid . quantity variable with the locality.
Aqueous vapour . quantity variable with the tem-
perature and humidity.
Ammonia ... a trace.
We said at present, because, when the Earth was
molten, the atmosphere must have been very different.
THE SOLAR SYSTEM. 87
We had, let us imagine, close to the still glowing crust —
composed perhaps of acid silicates —a dense vapour, com-
posed of compounds of the materials of the crust which
were volatile only at a high temperature ; the vapour of
chloride of sodium, or common salt, would be in large
quantity ; above this, a zone of carbonic acid gas ; above
this again a zone of aqueous vapour, in the form of steam ;
and lastly, the nitrogen and oxygen.*
As the cooling went on, the lowest zone, composed of
the vapour of salt, and other chlorides, would be con-
densed on the crust, covering it with a layer of these sub-
stances in a solid state. Then it would be the turn of the
steam to condense too, and form water ; it would fall on
the layer of salt, which it would dissolve, and in time the
oceans and seas would be formed, which would conse-
quently be salt from the first moment of their appearance.
Then, in addition to the oxygen and nitrogen which still
remain, we should have the carbonic acid, which, in the
course of long ages, was used up by its carbon going to form
the luxurious vegetation, the pressed remains of which
is the coal which warms us, and does nearly all our work.
2O9. Now it is the presence of vapour in our lower
atmosphere which renders life possible. When the surface
of the Earth was hot enough to prevent the formation of
the seas, as the water would be turned into steam again
the instant it touched the surface, there could be no life.
Again, if ever the surface of the Earth be cold enough to
freeze all the water and all the gaseous vapour in the atmo-
sphere, life — as we have it — would be equally impossible.
If this be true, all the Earth's history with which we
are acquainted, from the dawn of life indicated in what
geologists call the oldest rocks, down to our own time,
and perhaps onwards for tens of thousands of years,
* David Forbes, in the Geological Magazine, vol. iv. p. 439.
88 ASTRONOMY.
is only the history of the Earth between the time at
which its surface had got cold enough to allow steam to
turn into water, and that at which its whole mass will be
so cold that all the water on the surface, and all the vapour
of water in the atmosphere, will be turned into ice.
210. The nebular hypothesis here comes in and shows
us how, prior to the Earth being in a fluid state, it existed
dissolved in a vast nebula, the parent of the Solar System ;
how this nebula gradually contracted and condensed,
throwing off the planets one by one ; and how the central
portion of the nebula, condensed perhaps to the fluid
state, exists at present as the glorious heat-giving Sun.
Although, therefore, we know that stars give out light
because they are white-hot bodies, and that planets are
not self-luminous because they are comparatively cold
bodies, we must not suppose that planets were always
cold bodies, or that stars will always be white-hot bodies.
Indeed, as we have shown, there is good reason for sup-
posing that all the planets were once white-hot, and gave
out light as the Sun does now.
LESSON XVI. — THE MOON : ITS SIZE, ORBIT, AND
MOTIONS : ITS PHYSICAL CONSTITUTION.
211. The Moon, as we have already seen, is one of the
satellites, or secondary bodies ; and although it ap-
pears to us at night to be so infinitely larger than the fixed
stars and planets, it is a little body of 2,153 miles in
diameter ; so small is it, that 49 moons would be required
to make one earth, 300,000 earths being required, as
we have seen, to make one sun !
212. Its apparent size, then, must be due to its near-
THE SOLAR SYSTEM. 89
ness. This we find to be the case. The Moon revolves
round the Earth in an elliptic orbit, as the Earth revolves
round the Sun, at an average distance of only 238,793
miles, which is equal to about 10 times round our planet.
As the Moon's orbit is elliptical, she is sometimes nearer
to us than at others. The greatest and least distances
are 251,947 and 225,719 miles: the difference is 26,228.
When nearest us, of course she appears larger than at
other times, and is said to be in perigee (irepi near, and
yrj the Earth) ; when most distant, she is said to be in
apogee (airo from, and yrj).
213. The Moon travels round the Earth in a period of
27 d. 7h. 43m. u^s. As we shall see presently, she re-
quires more time to complete a revolution with respect to
the Sun, which is called a lunar month, lunation, or
synodic period.
214-. The Moon, like the planets and the Sun, rotates
on an axis ; but there is this peculiarity in the case of
the Moon, namely, that her rotation and her revolution
round the Earth are performed in equal times, that— is,
in 27 d. 7h. 43m. Hence we only see one side of our
satellite. But, as the Moon's axis is inclined i° 32' to
the plane of its orbit, we sometimes see the region round
one pole, and sometimes the region round the other. This
is termed the libration in latitude. There are also a
libration in longitude, arising from the fact, that though
its rotation is uniform, its rate of motion round the Earth
varies, so that we sometimes see more of the western edge
and sometimes more of the eastern one ; and a daily
libration, due to the Earth's rotation, carrying the ob-
server to the right and left of a line joining the centres of
the Earth and Moon. When on the right, or west, of this
line, we should of course see more of the western edge of
the Moon; when to the left, in the case of an eastern
position, we should see more of the eastern edge.
90 ASTRONOMY.
215. The plane in which the Moon performs her
journey round the Earth is inclined 5° to the plane of the
ecliptic, or the plane in which the Earth performs her
journey round the Sun (Art. 105) . The two points in which
the Moon's orbit, or the orbit of any other celestial body,
intersects the Earth's orbit, are called the nodes. The
line joining these two points is called the line of nodes.
The node at which the body passes to the north of the
ecliptic is called the ascending node, the other the
descending node.
216. The motions of the Moon, as we shall see by and
by, are very complicated. We may get an idea of its
path round the Sun if we imagine a wheel going along
a road to have a pencil fixed to one of its spokes, so as
to leave a trace on a wall : such a trace would consist
of a series of curves with their concave sides
downwards, and such is the Moon's path with regard
to the Sun.
217. Besides the bright portion lit up by the Sun, we
sometimes see, in the phases which immediately precede
and follow the New Moon, that the obscure part is
faintly visible. This appearance is called the " Earth
shine" (Lumen incinerosum, Lat.; Lumiere cendree, Fr.),
and is due to that portion of the Moon reflecting to us
the light it receives from the Earth. When this faint
light is visible — when the " Old Moon "is seen in the "New
Moon's arms " — the portion lit up by the Sun seems to
belong to a larger moon than the other. This is an effect
of what is called irradiation, and is explained by the
fact that a bright object makes a stronger impression on
the eye than a dim one, and appears larger the brighter it is.
218. The average of four estimations gives the Moon's
light as -nrfVn? °f tnat °f tne ^un> so we should want
547,513 full moons to give as much light as the Sun does ;
and as there would not be room to place such a large
THE SOLAR SYSTEM. 91
number in the one-half of the sky which is visible to us,
as the new Moon covers ^$m of it:> * follows that the
light from a sky full of moons would not be so bright as
sunshine.
219. At rising or setting, the Moon sometimes appears
to be larger than it does when high up in the sky. This
is a delusion, and the reverse of the fact ; for, as the Earth
is a sphere, we are really nearer the Moon by half the
Earth's diameter when the part of the Earth on which we
stand is underneath it ; as at moonrise or moonset we are
situated, as it were, on the side of the Earth, half-way
between the two points nearest to and most distant from
the Moon. Let the reader draw a diagram, and reason
this out.
220. Now a powerful telescope will magnify an object
i, coo times ; that is to say, it will enable us to see it as if it
were a thousand times nearer than it is: if the Moon were
1,000 times nearer, it would be 240 miles off, consequently
astronomers can see the Moon as if it were situated at a
little less than that distance, as it is measured from centre
to centre, and we look from surface to surface. In con-
sequence of this comparative nearness, the whole of the
surface of our satellite turned towards us has been studied
and mapped witli considerable accuracy.
221. With the naked eye we see that some parts of the
Moon are much brighter than others ; there are dark
patches, which, before large telescopes were in use, were
thought to be, and were named, Oceans, Gulfs, and so on.
The telescope shows us that these dark markings are
smooth plains, and that the bright ones are ranges of
mountains and hill country broken up in the most tremen-
dous manner by volcanoes of all sizes. A further study
convinces us that the smooth plains are nothing but oki
sea-bottoms. In fact, once upon a time the surface of the
Moon, like our Earth, was partly covered with water, and
92 ASTRONOMY.
the land was broken up into hills and fertile valleys ; as
on the Earth we have volcanoes, so did it once happen in
the Moon, with the difference that there the size of the
volcanoes and the number and activity of them were far
beyond anything we can imagine : our largest volcanic
mountain Etna is a mere dwarf compared with many on
the Moon.
222. The best way of seeing how the surface of our
satellite is broken up in this manner, is to observe the
terminator — the name given to the boundary between
the lit-up and shaded portions : along this line the moun-
tain peaks are lit up, while the depressions are in shade,
and the shadows of the mountains are thrown the greatest
distance on the illuminated portion. The heights of the
mountains and depths of the craters have been measured
by observing the shadows in this manner.
223. Besides the mountain-ranges and crater-moun-
tains, there are also walled plains, isolated peaks, and
curious markings, called rilies. The principal ranges,
craters, and walled plains have been named after distin-
guished philosophers, astronomers, and travellers.
224. The diameter of the walled plain Schickard, near
the south-east limb or edge of the Moon, is 133 miles.
Clavius and Grimaldi have diameters of 142 and 138
miles respectively. Here is a table of the height of some
of the peaks, with that of some of our terrestrial ones, for
comparison : —
Feet
Dorfel 26,691
Ramparts of ( measured from the ) g
Newton ( floor of the crater }
Eratosthenes (central cone) 15)75°
Mont Blanc 15,870
Snowdon 3>5°°
Beer and Madler have measured thirty-nine mountains
THE SOLAR SYSTEM. 93
higher than Mont Blanc. It must be recollected also
that as the Moon is so much smaller than the Earth, the
proportion of the height of a mountain to the diameter is
much greater in the former.
225. As far as we know, with possibly one exception,
which is not yet established, the volcanoes are now all
extinct ; the oceans have disappeared ; the valleys are no
longer fertile ; nay, the very atmosphere has apparently
left our satellite, and that little celestial body which pro-
bably was once the scene of various forms of life now no
longer supports them.
This may be accounted for by supposing (see Art. 191)
that, on account of the small mass of the Moon, its original
heat has all been radiated into space (as a bullet will take
less time to get cold than a cannon-ball).
226. The rilles, of which 425 are now known, are
trenches with raised sides more or less steep. Besides
the rilles, at full Moon, bright rays are seen, which seem
to start from the more prominent mountains. Some of
these rays are visible under all illuminations ; one which,
emanating from Tycho, crosses a crater on the north-
east of Fracastorius, is not only distinctly visible when
the terminator grazes the west edge of Fracastorius, but
is even brighter as the terminator approaches it. Those
emanating from Tycho are different in their character
from those emanating from Copernicus, while those
from Proclus form a third class.
Mr. Nasmyth has been able to produce somewhat
similar appearances on a glass globe by filling it with
cold water, closing it up, and plunging it into warm
water. This causes the inclosed cold water to expand
very slowly, and the globe eventually bursts, its weakest
point giving way, forming a centre of radiating cracks
in a similar manner to the fissures, if they be fissures, in
the Moon.
94 ASTRONOMY.
227. We say that the Moon has apparently no atmo-
sphere ; (i) because we never see any clouds there, and
(2) because, when the Moon's motion causes it to travel
over a star, or to occult it, as it is called, the star disap-
pears at once, and does not seem to linger on the edge,
as it would do if there were an atmosphere.
228. As the Moon rotates on her axis, as we do, only
more slowly, the changes of day and night occur there as
here ; but instead of being accomplished in 24 hours, the
Moon's day is 29^ of our days long, so that each portion
of the surface is in turn exposed to, and shielded from,
the Sun for a fortnight ; as there is no atmosphere either
to shield the surface or to prevent radiation, it has been
conjectured that the surface is, in turn, hotter than boiling
water, and colder than anything we have an idea of.
In Plate VI. we give a view of the crater Copernicus,
one of the most prominent objects in the Moon. The
details of the crater itself, and of its immediate neighbour-
hood, represented in the drawing, reveal to us unmis-
takeable evidences of volcanic action. The floor of the
crater is seen to be strewn over with rugged masses, while
outside the crater-wall (which on the left-hand side casts
a shadow on the floor, as the drawing was taken soon
after sunrise at Copernicus, and the Sun is to the left)
many smaller craters, those near the edge forming a
regular line, are distinctly visible. Enormous unclosed
cracks and chasms are also distinguishable. The depth
of the crater floor, from the top of the wall, is 1 1,300 feet ;
and the height of the wall above the general surface of
the moon is 2,650 feet. The irregularities in the top of
the wall are well shown in the shadow. The scale of miles
attached to the drawing shows the enormous propor-
tions of the crater.
LI \ \h < RATE]
COl'KRNICUS
Tlale'VL
.Tp Tn«v. Ma Tn-yth F, fl rr, RrnT*
96 ASTRONOMY.
lying to the right, as seen from the Earth ; at D we shall
see the lit-up portion lying to the left, looking from the
Earth. These positions are those occupied by the Moon
at the First Quarter and Last Quarter respectively.
When the Moon is at E and F we shall see but a small
Fig. 14. — Phases of the Moon.
part of the lit-up portion, and we shall get a crescent
Moon, the crescent in both cases being turned to the
Sun. At G and H the Moon will be gibbous.
231. So that the history of the phases is as follows : —
New Moon. The Moon is invisible to us, because the
Sun is lighting up one side and we are on
the other.
THE SOLAR SYSTEM. 97
Crescent Moon. We just begin to see a little of the illumi-
nated portion, but the Moon is still so
nearly in a line with the Sun, that we
only catch, as it were, a glimpse of the
side turned towards the Sun, and see the
Moon herself for a short time after sunset.
First Quarter. As seen from the Moon, the Earth and
Sun are at right angles to each other.
When the Sun sets in the west, the Moon
is south. Hence, as the illumination is
sideways, the right hand side of the Moon
is lit up.
Gibbous Moon. The Moon is now more than half lighted
up on the right-hand side.
Full Moon. The Earth is now between the Sun and
Moon, and therefore the entire half of
the Moon which is illuminated is visible.
232. From Full Moon we return through the Second
Quarter and other similar phases to the New Moon, when
the cycle recommences. So that, from New Moon the
illuminated portion of our satellite waxes, or increases
in size, till Full Moon, and then wanes, or diminishes,
to the next New Moon ; the illuminated portion, except
at Full Moon, being separated from the dark one by
a semi-ellipse, called, as we have seen (Art. 222), the
terminator.
233. In Fig. 14 we supposed that the Moon's motion
was performed in the plane of the ecliptic. Our readers
now know (Art. 215) that this is not the case : if it were
so, every Full Moon would put out the Sun ; and as the
Earth, and every body through which light cannot pass,
both on the Earth and off it, casts a shadow, every New
Moon would be hidden in that shadow. These appear-
ances are called eclipses, and they do happen sometimes.
H
98
ASTRONOMY.
Let us see if we can show under what circumstances they
do happen. One-half of the Moon's journey is performed
above the plane of the ecliptic, one-half below it ; hence
at certain times — twice in each revolution — the Moon is
in that plane, at those parts of it called the nodes. Now,
if the Moon at that time happens to be new or full — that
is, in line with the Earth and Sun —
in one case we shall have an eclipse
of the Sun, in the other we shall have
an eclipse of the Moon. This will
be rendered clear by the accompany-
ing figure. We have the Sun at
bottom, the Earth at top, and the
Moon in two positions marked A and
B, the level of the page representing
the level, or plane, of the ecliptic. We
suppose therefore in both cases that
the Moon is at a node, — that is, on
that level, neither above nor below it.
234. At A, therefore, the Moon
stops the Sun's light, its shadow falls
on a part of the Earth ; and the
people, therefore, who live on that
particular part of it where the shadow
falls cannot see the Sun, because the
Moon is in the way. Hence we shall
have what is called an eclipse of
the Son.
235. At B the Moon is in the
shadow of the Earth cast by the Sun ;
therefore the Moon cannot receive
any light from the Sun, because the
Earth is in the way. Hence we shall
have what is called an eclips^ if the
Moon.
SUN
/•' g 15.— Eclipses of the
Sun and Moon.
THE SOLAR SYSTEM. 99
236. It will easily be seen from the figure, that whereas
the eclipse of the Moon by the shadow of the much larger
Earth will be more or less visible to the whole side of
the Earth turned away from the Sun, the shadow cast
by the small Moon in a solar eclipse is, on the contrary,
so limited, that the eclipse is only seen over a small
area.
237. In the figure two kinds of shadows are shown,
one much darker than the other ; the latter is called the
umbra, the former the penumbra. If the Sun were a
point of light merely, the shadow would be all umbra ; but
it is so large, that round the umbra, where no part of the
Sun is visible, there is a belt where a portion of it can be
seen ; hence we get a partial shadow, which is the meaning
of penumbra. This will be made quite clear if we get
two candles to represent any two opposite edges of the
Sun, place them rather near together, at equal distances
from a wall, and observe the shadow they cast on the wall
from any object ; on either side the shadow thrown by
both candles will be a shadow thrown only by one.
238. In a total eclipse of the Moon, as the Moon travels
from west to east, we first see the eastern side of the
Moon slightly dim as she enters the penumbra ; this is
the first contact with the penumbra, spoken of in
almanacs. At length, when the real umbra is reached,
the eastern edge becomes almost invisible ; we have the
first contact with the dark shadow; the circular
shape of the Earth's shadow is distinctly seen, and at
last she enters it entirely. When the Moon passes, how-
ever, into the shadow of the Earth, it is scarcely ever quite
obscured; the Sun's light j° bent by the Earth's atmo-
sphere towards the Moon, and sometimes tinges it with a
ruddy colour.
A total eclipse of the Moon may last about if hours.
When the Moon again leaves the umbra we have the last
II 2
loo ASTRONOMY.
contact with the dark shadow; and after the last
contact with the penumbra, the eclipse is over.
239. If the Moon is not exactly at a node, we shall
only get a partial eclipse of the Me on, the degree of
eclipse depending upon the distance from the node. For
instance, if the Moon is to the north of the node, the
lower limb may enter the upper edge of the penumbra or
of the umbra ; if to the south of the node, the upper
portion will be obscured.
LESSON XVI II. — ECLIPSES (continued}. ECLIPSES OF
THE SUN. TOTAL ECLIPSES AND THEIR PHENO-
MENA. CORONA. RED-FLAMES.
24-O. In a total eclipse of the Sun, the diameter of the
shadow which falls on the Earth is never large, averaging
about 150 miles ; and as the Moon, which throws the
shadow, revolves from west to east in a month, while the
Earth's surface, on which it falls, rotates from west to east
in a day, the shadow travels more slowly than the surface,
and so appears to sweep across it from east to west with
great rapidity. The longest time an eclipse of the Sun
can be total at any place is seven minutes, and of course
it is only visible at those places swept by the shadow.
Hence, in any one place total eclipses of the Sun are of
very rare occurrence ; in London, for instance, there has
been no total eclipse of the Sun since 1715.
24-1. In eclipses of the Sun there are no visible effects
of umbra and penumbra seen on the Sun itself; we have
the real (though invisible) Moon eating into the real and
visible Sun, the western edge of the Sun in the case
of total eclipses being first obscured. The obscuration
THE SOLAR SYSTEM. roi
increases until the Moon covers all the Sun, and soon
afterwards the western edge of the Sun reappears.
24-2. As in the case of the Moon, there are other
eclipses besides total ones. To explain this we must give
a few figures. As both Sun and Moon are round, or
nearly so, the shadow from the latter is round ; and as the
Sun is larger than the Moon, the shadow ends in a point.
The shape of the shadow is. in fact, that of a cone —
hence the term " cone of shadow." Now, the length of
this cone varies with the Moon's distance from the Sun :
when nearest, the Moon will of course throw the shortest
shadow. The lengths are about as follow :— ^.}^
When the Moon and Sun are nearest together . 230,000
„ „ „ furthest apart . . . 238,000
But in Art. 212 we saw that the distance between the
Earth and Moon varied as follows : —
Miles.
When the Moon and Earth are nearest together . 225,719
„ „ „ furthest apart . .251,947
Hence, when the Moon is furthest from the Earth, or in
apogee, the shadow thrown by the Moon is not long
enough to reach the Earth ; at such times the Moon looks
smaller than the Sun, and if she be at a node, we shall
have an annular eclipse — that is, there will be a ring
(annulus, Lat. ring) of the Sun visible round the Moon
when the eclipse would otherwise have been total.
243. There may be partial eclipses of the Sun, for the
same reason as we have partial eclipses of the Moon ; only
as the Moon is not exactly at the node in one case, she
does not get totally eclipsed, because she does not pass
quite into the shadow of the Earth ; and in the other,
the Sun does not get totally eclipsed, because the Moon
does not pass exactly between us and the Sun.
24-4.. The nodes of the Moon are not stationary, but
move backwards upon the Moon's orbit, a complete revo-
102 ASTRONOMY.
lution taking place with regard to the Moon in 18 year*
2 19 days, nearly. The Moon in her orbit, therefore, meets
the same node again before she arrives at the same place
with regard to the Sun again, one period being 27 d. 5h.6m.,
called the nodical revolution of the Moon; and the other,
29 d. I2h. 44m., called the synodical revolution of the
Moon, in which it regains the same position with regard
to the Sun. The node is in the same position with regard
to the Sun after an interval of 346 d. I4h. 52111. This is
called a synodic revolution of the node. Now it so hap-
pens that nineteen synodic.il revolutions of the node, after
which period the Sun and node would be alike situated ;
are equal to 223 synodical revolutions of the Moon, after
which period the Sun and Moon would be alike situated :
so that, if we have an eclipse at the beginning of the
period, we shall have one at the end of it, the Sun, Moon,
and node having got back to their original positions.
This period of 18 years 219 days is a cycle of the Moon,
known to the ancient Chaldeans and Greeks under the
name of Saros, and by its means eclipses were roughly
predicted before astronomy had made much progress.
24-5. A total eclipse of the Sun is at once one of the
most awe-inspiring and grandest sights it is possible for
man to witness. As the eclipse advances, but before the
totality is complete, the sky grows of a dusky livid, or
purple, or yellowish crimson, colour, which gradually gets
darker and darker, and the colour appears to run over
large portions of the sky, irrespective of the clouds. The
sea turns lurid red. This singular colouring and darken-
ing of the landscape is quite unlike the approach of night,
and gives rise to strange feelings of sadness. The Moon's
shadow is seen to sweep across the surface of the Earth,
and is even seen in the air ; the rapidity of its motion and
its intenseness produce a feeling that something material
is sweeping over the Earth at a speed perfectly frightful.
arren Ee La.Eue."F.E.S.
THE SOLAR SYSTEM. 103
All sense of distance is lost, the faces of men assume a
livid hue, fowls hasten to roost, flowers close, cocks crow,
and the whole animal world seems frightened out of its
usual propriety.
24-6. A few seconds before the commencement of the
totality the stars burst out ; and surrounding the dark
Moon on all sides is seen a glorious halo, generally of a
silver-white light; this is called the corona. It is slightly
radiated in structure, and extends sometimes beyond the
Moon to a distance equal to our satellite's diameter.
Besides this, rays of light, called aigrettes, diverge
from the Moon's edge, and appear to be shining through
the light of the corona. In some eclipses some parts of
the corona have reached to a much greater distance from
the Moon's edge than in others.
247. It is supposed that the corona is the Sun's atmo-
sphere, which is not seen when the Sun itself is visible,
owing to the overpowering light of the latter.
24-8. When the totality has commenced, apparently
close to the edge of the Moon, and therefore within the
corona, are observed fantastically- shaped masses, full lake-
red, fading into rose-pink, variously called red-flames
and red-prominences. Two of the most remarkable of
these hitherto noticed were observed in the eclipse of
1851. They have thus been described by the Rev.
W. R. Dawes :—
" A bluntly triangular pink body [was seen] suspended,
as it were, in the corona. This was separated from the
Moon's edge when first seen, and the separation increased
as the Moon advanced. It had the appearance of a large
conical protuberance, whose base was hidden by some
intervening soft and ill-defined substance. ... To the
north of this appeared the most wonderful phenomenon
of the whole : a red protuberance, of vivid brightness and
very deep tint, arose to a height of perhaps if' when first
104 ASTRONOMY.
seen, and increased in length to 2' or more, as the
Moon's progress revealed it more completely. In shape
it somewhat resembled a Turkish cimeter, the northern
edge being convex, and the southern concave. Towards
the apex it bent suddenly to the south, or upwards, as
seen in the telescope. ... To my great astonishment,
this marvellous object continued visible for about five
seconds, as nearly as I could judge, after the Sun began
to reappear."
24-9. It has been definitely established that these pro-
minences belong to the Sun, as those at first visible on
the eastern side are gradually obscured by the Moon,
while those on the western are becoming more visible,
owing to the Moon's motion from west to east over the
Sun. The height of some of them above the Sun's sur-
face is upwards of 40,000 miles.
25O. It is thought that these red-prominences are
incandescent clouds floating in the Sun's atmosphere, or
resting upon the photosphere ; but this has not as yet been
definitely established.
LESSON XIX. — THE OTHER PLANETS COMPARED WITH
THE EARTH. PHYSICAL DESCRIPTION OF MARS.
251. We are now in a position to examine the other
planets of our system, and to bring the facts taught us by
our own to bear upon them. In the case of all the planets
we have been able to ascertain the facts necessary to de-
termine the elements of their revolution round the Sun ;
that is to say, the time in which the complete circuit round
the common luminary is accomplished, and the shape and
position of their orbits with regard to our own. Now the
Plate T2ZZ"
Warren De La Rue del
S.RusseH Sculp.
THE SOLAR SYSTEM. 105
shape of the orbit depends upon the degree of its ellipticity
— for all are elliptical — and its position upon the distance
of the planet from the Sun, and the degree in which the
plane of each orbit departs from our own. When we
have, in addition to these particulars, the position of the
nodes — the points in which the orbit intersects the plane
of our orbit — and the position of the perihelion points,
we have all the materials necessary for calculation or for
making a diagram of the planet's path.
252. Still, however satisfactory our examination of the
planets has been with regard to their revolution round the
Sun, we are compelled to state that when we wish to in-
quire into their rotations on their axes, the length of their
days, their seasons, and their physical constitutions, the
knowledge as yet acquired by means of the telescope is
far from complete. Thus, of the planets Mercury and
Venus we have nothing certain to tell on these matters ;
they are both so lost in the Sun's rays, and so refulgent in
consequence of their nearness to that body, that our ob-
servation of them, of Mercury especially, has been baffled.
Of the same class of facts in the case of Uranus and
Neptune we are equally ignorant, but for a different
reason. At our nearest approach to Uranus we are up-
wards of 1,700,000,000 miles away from that planet ; at
our nearest approach to Neptune we are upwards of
2,600,000,000 miles away, and we cannot be surprised that
our telescopes fail us in delicate observations at such dis-
tances. Still, in the case of Uranus, we have been able to
assume some facts from the motions of his moons.
253. With regard however to Mars, Jupiter, and Saturn,
the planets whose orbits are nearest to our own, our
information is comparatively full and complete. For
instance, we can for these planets give the following in-
formation in addition to that stated in Arts. 139 and 140,
and Table II. of the Appendix.
106 ASTRONOMY.
Length of Day. Inclination of
H. M. S. Axis.
Mars . . . 24 37 22 . . . 28° 51' o"
Jupiter .. 95521... 3 40
Saturn . . 10 29 17 . . . 28 10 o
The first column requires no explanation. We see,
however, at once that the day in Mars is nearly equal to
our own, while in the large planets, Jupiter and Saturn, it
is not half so long. Now the revolutions of these planets
round the Sun are accomplished as follow : —
Mars in 686 of our days.
Jupiter in 4-333 „ »
Saturn in 10,759 » »
We can therefore easily find the number of days ac-
cording to the period of rotation of each planet, which
go to make each planetary year : thus in Saturn's year
there are 24,584 Saturnian days, or 67 times more days
than in our own.
254. In the second column the inclination of the
planets' axes of rotation is given. It will be recol-
lected that the inclination of our own is 23^°, and that it
is on this inclination that our seasons depend. It will
be seen at once therefore that Mars and Saturn are much
like the Earth in this respect, and that Jupiter is a planet
almost without seasons, for the inclination of its axis is
only 3°, while that of Uranus is 100°. The axis of rotation
of Uranus, in fact, lies almost in the plane of its orbit.
255. As in the case of the Earth, we find in many in-
stances the axis of rotation, or polar diameter, of the other
planets shorter than the equatorial diameter. The amount
of polar compression, — that is, the amount of flattening,
by which the polar diameter is less than the equatorial
one, — measured in fractions of the latter, is as follows : —
THE SOLAR SYSTEM. 107
Mercury
Venus
Earth
Mars .
Jupiter .
Saturn
Uranus
Neptune
From this Table we learn that if the equatorial dia-
meter of Mercury be taken as 29, the polar one is only'
28 : in the cases of Jupiter and Saturn, the diameters are
as 17 to 1 6 and 9 to 8, respectively. In these two last the
rotation is very rapid (Art. 253) ; and this great flattening
is what we should expect from the reasoning in Art. 196
256. We now come to what we can glean of the
physical structure of the planets as seen in the telescope
when they are nearest the Earth. Let us begin with Mars.
We give in Plate IX. two sketches, taken in the year 1862.
Here at once we see that we have something strangely
like the Earth. The shaded portions represent water,
the lighter ones land, and the bright spot at the top of
the drawings is probably snow lying round the south pole
of the planet, which was then visible.
257. The two drawings represent the planet as seen in
an astronomical telescope, which inverts objects so that
the south pole of the planet is shown at top. The upper
drawing was made on the 25th of September, the lower
one on the 23d. In the upper one a sea is seen on the
left, stretching down northwards ; while, joined on to it, as
the Mediterranean is joined on to the Atlantic, is a long
narrow sea, which widens at its termination.
In the lower drawing this narrow sea is represented
on the left. The coast-line on the right strangely reminds
one of the Scandinavian peninsula, and the included
Baltic Sea.
258. It will be now easy to understand how we have
been able to determine the length of the day and the
inclination of the axis. We have only to watch how long
308 ASTRONOMY.
it takes one of the spots near the equator of each planet
to pass from one side to the other, and the direction it
takes, to get at both these facts.
259. Mars not only has land and water and snow like
us, but it has clouds and mists, and these have been
watched at different times. The land is generally reddish
when the planet's atmosphere is clear ; this is due to the ab-
sorption of the atmosphere, as is the colour of the setting
Sun with us. The water appears of a greenish tinge.
260. Now, if we are right in supposing that the bright
portion surrounding the pole be ice and snow, we ought to
see it rapidly decrease in the planet's summer. This is
actually found to be the case, and the rate at which the
thaw takes place is one of the most interesting facts to be
gathered from a close study of the planet. In 1862 this
decrease was very visible. The summer solstice of Mars
occurred on the 3oth of August, and the snow-zone was
observed to be smallest on the nth of October, or forty-
two of our days after the highest position of the Sun. This
very rapid melting may be ascribed to the inclination of
the axis, which is greater than with us; to the greater
eccentricity of the planet's orbit ; and to the fact that the
summer time of the southern hemisphere occurs when the
planet is near perihelion,
261. Far a reason that will be easily understood when
we come to deal with the effect of the Earth's revolution
round the Sun on the apparent positions and aspects of
the planets, we sometimes see the north pole, and some-
times the south pole of Mars, and sometimes both : when
either pole only is visible, the features, which appear to
pass across the planet's disc in about twelve hours — that
is, half the period of the planet's rotation — describe curves
with the concave side towards the visible pole. When both
poles are visible they describe straight lines, exactly as in
the case of the Sun (Art. 106). These changes enable all
Plate IX.
MARS in 1862.
THE SOLAR S YSTEM. \ \ \
the surface to be seen at different times, and maps of
Mars have been constructed, the exact position of the
features of the planet being determined by their latitude
and longitude, as in the case of the Earth.
262. But although we see in Mars so many things that
remind us of our planet, and show us that the extreme
temperatures of the two planets are not far from equal,
a distinction must be drawn between them. In conse-
quence of the great eccentricity of the orbit of Mars, the
lengths of the various seasons are not so equal as with us,
and, owing to the longer year, they are of much greater
extent. In the northern hemisphere of the planet they
are as under : —
days. hrs.
Spring lasts .... 191 8
Summer „ . . . . 181 o
Autumn „ .... 149 8
Winter „ . . . . 147 o
As we must reverse the seasons for the southern hemi-
sphere, spring and summer, taken together, are 76 days
longer in the northern hemisphere than in the southern.
LESSON XX. — THE OTHER PLANETS COMPARED WITH
THE EARTH (continued). JUPITER: HIS BELTS
AND MOONS. SATURN : GENERAL SKETCH OF HIS
SYSTEM.
263. Let us now pass on to Jupiter, by far the largest
planet in the system, and bright enough sometimes, in
spite of its great distance, to cast a shadow like Venus.
The first glance at the drawing (Plate X. Fig. i) will
show us that we have here something very unlike Mars ;
H2 ASTRONOMY.
and this is the case The planet Jupiter is surrounded by
an atmosphere so densely laden with clouds, that of the
actual planet itself we know nothing.
What are generally known as the belts of Jupiter are
dusky streaks which cross a brighter background in direc-
tions generally parallel to the planet's equator. And for the
most part, the largest belts are situated on either side of it,
in exactly the same way as the two belts of Trade-Winds
on the Earth lie on either side of the belt of Equatorial
Calms and rains. Outside these, again, we get represen-
tatives of the Calms of Cancer and Capricorn, although
these are not so regularly seen, the portion of the planet's
surface polewards of the two belts being liable to great
changes of appearance, sometimes in a very short time.
The portions of the atmosphere representing the terres-
trial calm-belts sometimes exhibit a beautiful rosy tint,
the equatorial one especially.
264. The variations of this cloudy atmosphere lend
great variety to the appearance of the planet at different
times; the belts are sometimes seen in large numbers,
and extend almost to the poles. Besides the belts, some-
times bright spots, sometimes dark ones, are seen, which
have enabled us to determine the period of the planet's
rotation, which, as we have seen, is very rapid — so rapid,
that on the equator an observer would be carried round
at the rate of 467 miles a minute, instead of 17 as on
the Earth. We can easily understand that this rapid
rotation would break the cloudy surface into belts more
than with us, or as is the case of Mars ; in the latter
planet, indeed, no trace of cloud-belts has as yet been
detected ; their absence is perhaps due to its slow rotation
and small size.
265. Although all astronomers do not agree that the
surface of the planet is never seen, there are many strong
reasons why it should not be seen. In the first place,
JUPITER,
ratten DC- -
SATITRK.
THE SOLAR SYSTEM. 113
Mars and the Earth, whose atmospheres are nearly alike,
have nearly the same densities (Art. 145), while, in the case
of Jupiter and Saturn — the belts of which latter planet,
as far as we can observe them, resemble Jupiter's — the
density, as calculated on the idea that what we see is all
planet, is only about one-fifth that of the Earth ; and as
the density of the Earth is 5^ times that of water, it
follows that the densities of the two planets in question
are not far off that of water.
266. Now, if we suppose that the apparent volume of
Jupiter (and similarly of Saturn) is made up of a large
shell of cloudy atmosphere and a kernel of planet, there
is no reason why the density of the real Jupiter (and
of the real Saturn) should vary very much from that of
the Earth or Mars, and this would save us from the water-
planet hypothesis. Moreover, a large shell of cloudy
atmosphere is precisely what our own planet was most
probably enveloped in, in one of the early stages of its
history (Art. 208).
267- In addition to the changing features of Jupiter
itself, the telescope reveals to us four moons, which as
they course along rapidly in their orbits, and as these
orbits lie nearly in the plane of the planet's orbit, lend a
great additional interest to
the picture. In the various
positions in their orbits the
satellites sometimes appear
at a great distance from the
primary ; sometimes they
come between us and the Fig l6._Juplter and his Moons
planet, appearing now as (general view).
bright and now as dark spots on its surface. At
other times they pass between the planet and the Sun,
throwing their shadows on the planet's disc, and
causing, in fact, eclipses of the Sun. They also enter
T
H4 ASTRONOMY.
into the shadow cast by the planet, and are therefore
eclipsed themselves ; and sometimes they pass behind the
planet, and are said to be o c c u 1 1 e d. Of these appearances
we shall have more to say by and by (Lesson XXXVI).
268. Referring to the sizes of these moons and their
distances from the planet, in Table III. of the Appendix,
it may be here added that, like our Moon, they rotate on
their axes in the same time as they revolve round Jupiter.
This has been inferred from the fact that their light varies,
and that they are always brightest and dullest in the same
positions with regard to Jupiter and the Sun.
269. In Plate X. the black spot is the shadow of a satel-
lite, and the satellite itself is seen to the left ; the passage
of either a satellite or shadow is called a transit. In a
solar eclipse, could we observe it from Venus, we should
see a similar spot sweeping over the Earth's surface.
270. We now come to Saturn; and here again, as in
the case of Jupiter, we come upon another departure
from Mars and the Earth. The planet itself, which is
belted like Jupi-
ter, is surrounded
not only by eight
moons, but by a
series of rings,
one of which, the
inner one, is trans-
parent! The belts
have been before
referred to (Art.
Fig, 17. — Saturn and his Moons (general view). ~£.c\ fV, A
not, therefore, detain us here ; and we may dismiss the
satellites — as their distances from Saturn, &c. are given
in Table III. of the Appendix — with the remark, that as
the equator of Saturn, unlike that of Jupiter, is greatly
THE SOLAR SYSTEM. ill
inclined to the ecliptic; transits, eclipses, and occulta-
tions of the satellites, the orbits of which for the most
part lie in that plane, happen but rarely.
271. It is to the rings that most of the interest of this
planet attaches. We may well imagine how sorely puzzled
the earlier observers, with their very imperfect telescopes,
were, by these strange appendages. . The planet at first
was supposed to resemble a vase ; hence the name Ansce,
or handles, given to the rings in certain positions of the
planet. It was next supposed to consist of three bodies,
the largest one in the middle. The true nature of the
rings was discovered by Huyghens in 1655, who announced
it in this curious form : —
"aaaaaaa ccccc d eeeee g h iiiiiii 1111 mm
nnnnnnnnn oooo pp q rr s ttttt uw.uu,"
which letters, transposed, read : —
" annulo cingitur, tcniti piano, nusquam cohaerente, ad
cclipticam inclinato"
There is nothing more encouraging in the history of
astronomy than the way in which eye and mind have
bridged over the tremendous gap vvhich separates us from
this planet. By degrees the fact that the appearance was
due to a ring was determined ; then a separation was
noticed dividing the ring into two ; the extreme thinness
of the ring came out next, when Sir William Herschel
observed the satellites "like pearls strung on a silver
thread;" then an American astronomer, Bond, discovered
that the number of rings must be multiplied we know not
how many fold. Next followed the making out of the
transparent ring by Dawes and Bond, in 1852 ; then the
transparent ring was discovered to be divided as the whole
system had once been thought to be ; last of all comes
evidence that the smaller divisions in the various rings are
subject to change, and that the ring-system itself is pro-
bably increasing in breadth, and approaching the planet.
I 2
ii6 ASTRONOMY.
LESSON XXL— THE OTHER PLANETS COMPARED WITH
THE EARTH (continued). DIMENSIONS OF SATURN
AND HIS RINGS. PROBABLE NATURE OF THE RINGS.
EFFECTS PRODUCED BY THE RINGS ON THE PLANET.
URANUS. NEPTUNE: ITS DISCOVERY.
The lower figure of Plate X. will give an idea of the
appearance presented by the planet and its strange and
beautiful appendage. It will be shown in the sequel
(Chap. IV.) how we see, sometimes one surface, and some-
times another, of the ring, and how at other times the
edge of it is alone visible.
272. The ring-system is situated in the plane of the
planet's equator, and its dimensions are as follow : —
Miles.
Outside diameter of outer ring . . . 166,920
Inside „ „ . . . 147,670
Distance from outer to inner ring . . 1,680
Outside diameter of inner ring . . . 144,310
Inside „ „ ... 109,100
Inside „ dark ring . . . 91,780
Distance from dark ring to planet . . 9,760
Equatorial diameter of planet . . . 72,250
So that the breadths of the three principal rings, and of
the entire system, are as follo\v : —
Miles.
Outer bright ring 9,625
Inner bright ring 17,605
Dark ring 8,660
Entire system 37,57°
and the distance between the two bright rings is 1,680
miles.
THE SOLA R S YS TEM. 1 1 7
In spite of this enormous breadth, the thickness of the
rings is not supposed to exceed 100 miles.
273. Of what, then, are these rings composed ? There
is great reason for believing that they are neither solid
nor liquid ; and the idea now generally accepted is
that they are composed of myriads of satellites, or little
bodies, moving independently, each in its own orbit, round
the planet ; giving rise to the appearance of a bright ring
when they are closely packed together, and a very dim
one when they are most scattered. In this way we may
account for the varying brightness of the different parts,
and for the haziness on both sides of the ring near the
planet (shown in Fig. 38 ), which is supposed to be due to
the bodies being drawn out of the ring by the attraction
of the planet.
274-. Although Saturn appears to resemble Jupiter in
its atmospheric conditions, unlike that planet, and like our
own Earth, its year, owing to the great inclination of its
axis, is sharply divided into seasons, which however are
here indicated by something else than a change of tem-
perature ; we refer to the effects produced by the presence
of the strange ring appendage. To understand these
effects, its appearance from the body of the planet must
first be considered. As the plane of the ring lies in the
plane of the planet's equator, an observer at the equator
will only see its thickness, and the ring therefore will
put on the appearance of a band of light passing through
the east and west points and the zenith. As the ob-
server, however, increases his latitude either north or
south, the surface of the ring- system will begin to be seen,
and it will gradually widen, as in fact the observer will
be able to look down upon it ; but as it increases in
width it will also increase its distance from the zenith,
until in lat 63° it is lost below the horizon, and between
this latitude and the poles it is altogether invisible.
n8 ASTRONOMY.
275- Now the plane of the ring always remains parallel
to itself, and twice in Saturn's year — that is, in two opposite
points of the planet's orbit — it passes through the Sun.
It follows, therefore, that during one-half of the revolution
of the planet one surface of the rings is lit up, and during
the remaining period the other surface. At night, there-
fore, in one case, the ring-system will be seen as an illumi-
nated arch, with the shadow of the planet passing over
it, like the hour-hand over a dial ; and in the other, if it
be not lit up by the light reflected from the planet, its
position will only be indicated by the entire absence of stars.
276. But if the rings eclipse the stars at night, they can
also eclipse the Sun by day. In latitude 40° we have
morning and evening eclipses for more than a year,
gradually extending until the Sun is eclipsed during the
whole day — that is, when its apparent path lies entirely in
the region covered by the ring ; and these total eclipses
continue for nearly seven years : eclipses of one kind or
another taking place for 8 years 292 days. This will give
us an idea how largely the apparent phenomena of the
heavens, and the actual conditions as to climates and
seasons, are influenced by the presence of the ring.
As the year of Saturn is as long as thirty of ours, it
follows that each surface of the rings is in turn deprived
of the light of the Sun for fifteen years.
277- We have now finished with the planets known to
the ancients; the remaining ones, Uranus and Neptune,
have been discovered in modern times — the former in
1781, by Sir Wm. Herschel, and the latter in 1846, inde-
pendently, by Professor Adams and M. Le Verrier.
278. Both these planets are situated at such enormous
distances from the Sun, and therefore from us, that
Uranus is scarcely, and Neptune not at all, visible to the
naked eye. Owing to this remoteness, nothing is known
of their physical peculiarities. We have already stated,
THE SOLAR SYSTEM. 119
ho \vever, that the motion of the satellites of Uranus is in
the opposite direction to that of all the other planetary
members of the system.
279. The discovery of the planet Neptune is one of the
most astonishing facts in the history of Astronomy. As
we shall see in the sequel, every body in our system
affects the motions of every other body ; and after Uranus
had been discovered some time, it was found that on
taking all the known causes into account, there was still
something affecting its motion ; it was suggested that this
something was another planet, more distant from the Sun
than Uranus itself. And the question was, where was this
planet, if it existed ?
When we come to consider the problem in all its
grandeur, we need not be surprised that two minds, who
felt themselves competent to solve it, should have inde-
pendently undertaken it. As far back as July 1841, we
find Mr. Adams determined to investigate the irregularities
of Uranus: early in September 1846, the new planet
had fairly been grappled. We find Sir John Herschel
remarking, " We see it as Columbus saw America from
the shores of Spain. Its movements have been felt
trembling along the far-reaching line of our analysis with
a certainty hardly inferior to ocular demonstration."
On the 29th July, 1846, the large telescope of the Cam-
bridge Observatory was first employed to search for the
planet in the place where Professor Adams's calculations
had assigned it. M. Le Verrier, in September, wrote to
the Berlin observers, stating the place where his calcula-
tion led him to believe it would be found : his theoretical
place and Professor Adams's being not a degree apart.
At Berlin, thanks to their star-maps, which had not yet
been published, Dr. Galle found the planet the same
evening, very near the position assigned to it by both
Astronomers.
120 ASTRONOMY.
LESSON XXII.— THE ASTEROIDS, OR MINOR PLANETS.
BODE'S-LAW. SIZE OF THE MINOR PLANETS: THEIR
ORBITS : HOW THEY ARE OBSERVED.
28O. If we write down —
o 3 6 12 24 48 96
and add 4 to each, we get
4 7 10 16 28 52 100
and this series of numbers represents very nearly the
distances of the ancient planets from the Sun, as fol-
lows i—-
Mercury, Venus, Earth, Mars, — , Jupiter, Saturn.
This singular connexion was discovered by Titius, and is
known by the name of Bode's-law, We see that the
fifth term has apparently no representative among the
planets. This fact acted so strongly on the imagination
of Kepler that he boldly placed an undiscovered one in
the gap. Up to the time of the discovery of Uranus the
undiscovered planet did not reveal itself: when it was
found, however, that the actual position of Uranus was very
well represented by the next term of the series, 196, it
was determined to make an organized search for it, and
for this purpose a society of astronomers was formed ; the
zodiac was divided into 24 zones, each zone being confided
to a member of the society. On the first day of the
present century a planet was discovered and named Ceres,
which, curiously enough, filled up the gap. But the
discovery of a second, third, and fourth, named respec-
tively Pallas, Juno, and Vesta, soon followed, and up
to the present time (February 1868) no less than 97 of
THE SOLAR SYSTEM. 121
these little bodies have been detected. A list of them,
with their symbols, will be found in the Appendix,
Table I.
281. None of these planets, except occasionally Ceres
and Vesta, can be seen by the naked eye ; and this brings
ir. at once to their chief characteristic — the largest minor
planet is but 228 miles in diameter, and many of the
smaller ones are less than 50.
282. The orbits of those hitherto discovered, for the
most part, lie nearer to Mars than Jupiter, and the orbits
in some cases are so elliptical, that if we take the extreme
distances into account, they occupy a zone 240,000,000
miles in width — the distance between Mars and Jupiter
being 336,000,000. The planet nearest the Sun is 0 Plora,
whose journey round the Sun is performed in 3^ years, at
a mean distance of 201,000,000 miles; the most distant
one is © Maximiliana, whose year is as long as 6£ of
ours, and whose mean distance is 313,000,000 miles.
283. Not only do some of the orbits approach those
of comets in the degree of eccentricity, but they resemble
them in another matter— their great inclination to the
ecliptic. The orbit of © Pallas, for instance, is inclined
34° to the plane of the ecliptic ; while © Mass ilia is
inclined but a few minutes of arc.
284. The minor planets lately discovered shine as stars
of the tenth or eleventh magnitude, and the only way in
which they can be detected, therefore, is to compare the
star-charts of different parts of the heavens with the
heavens themselves, night after night. Should any point
of light be observed not marked on the chart, it is imme-
diately watched, and if any motion is detected, the amount
and direction are determined. Some idea of the diligence
and patience required for this branch of observation may
be gathered from Fig. 18, which is a reduction of a part
of one of M. Chacornac's ecliptic charts. The faint
123 ASTRONOMY.
diagonal line shows the path of a minor planet across
that portion of the heavens represented.
Fig. 1 8. — Star Map, shuwing the path ot a Minor Planet.
285. With regard to the cause for the existence of these
little bodies, it has been suggested that they may be
THE SOLAR SYSTEM. 123
fragments cf a larger planet destroyed by contact with
some other celestial body. D'Arrest remarks : " One fact
seems, above all, to confirm the idea of an intimate rela-
tion between all the minor planets : it is, that if their
orbits are figured under the form of material rings, these
rings will be found so entangled that it would be possible,
by means of one among them, taken at hazard, to lift up
all the rest."
286. 0 Pallas has been supposed, from its hazy ap-
pearance, to be surrounded by a dense atmosphere, and
this may also be the case with the others, as their colours
are not the same. There are also evidences that some
among them rotate on their axes like the larger planets.
LESSON XXIII.— COMETS : THEIR ORBITS. SHORT-
PERIOD COMETS. HEAD, TAIL, COMA, NUCLEUS,
JETS, ENVELOPES. THEIR PROBABLE NUMBER AND
PHYSICAL CONSTITUTION.
287. We have seen that round the white-hot Sun cold
or cooling solid bodies, called planets, revolve ; that be-
cause they are cold they do not shine by their own light ;
that they perform their journeys in almost the same plane ;
tnat the shape of their orbit is oval or elliptical ; and
that they all move in one direction, — that is, from west
to east.
But these are not the only bodies which revolve round
the Sun. In addition to them there are masses, probably
white-hot, called comets, which do shine by their own
light ; which perform their journeys round the Sun in
every plane, in orbits which in some cases are so elon-
ited that they can scarcely be called elliptical, and — a
124
ASTRONOMY.
further point of difference — while some revolve round the
Sun in the same direction as the planets, others revolve
from east to west.
288. The orbit of a comet is generally best represented
by what is called a parabola; that is, an infinitely long
ellipse, which latter, like a circle, is a closed curve— whereas
the parabola may be regarded as an open one (Chap. IX.).
In the case of a comet whose whole orbit has been watched,
we know that orbit is elliptical. In the case of those
with parabolic orbits, we know not whence they come
or whither they are going, and therefore we cannot say
whether they will return or not. There are some comets
whose return may be depended upon and calculated with
certainty. Here is a list of some of them : —
: '
Comets.
Time of
Revolu-
tion.
Nearest
Approach
to the
Sun,
Greatest
Distance
from the
Sun.
Next
Return.
Encke's . . .
Years.
3*
32,000,000
387,000,000
1868
De Vice's . .
5*
110,000,000
475,000,000
1872
Winnecke's
5*
...
1869
Brorsen's . .
5i
64,000,000
537,000,000
1868
Blela's . . .
6*
82,000,000
585,000,000
1873
D' Arrest's . .
6i
...
...
1870
Faye's . . .
7i
192,000,000
603,000,000
1873
Mechain's .
13*
...
...
1871
Halley's . .
76! i 56,000, ooo
3,200,000,000
1910
289. These are called short-period comets. Of the
long-period comets we may instance the comets of 1858,
1811, and 1844, the times of revolution of which have
been estimated at 2,100, 3,000, and 100,000 years re-
spectively.
THE SOLAR SYSTEM.
125
290. From the table that we have given it will be seen
how the distance of these erratic bodies from the Sun
varies in different points of the orbit. Thus Encke's
comet is ten times nearer the Sun in perihelion than at
aphelion. Some comets, whose aphelia lie far beyond
the orbit of Neptune, approach so close to the Sun as
almost to graze its surface. Six Isaac Newton estimated
that the comet of 1680 approached so near the Sun that
its temperature was 2,000 times that of red-hot iron : at
the nearest approach it was but one-sixth part of the sun's
diameter from the surface. The comet of 1843 also made
a very near approach to the Sun, and was visible in broad
daylight.
291. We next come to what a comet is like. In
Fig. 19 we give a represen-
tation of Donati's comet,
visible in 1858, which will
make a general description
clear. The brighter part of
the comet is called the head,
or coma, and sometimes the
head contains a brighter
portion still, called the
nucleus. The tall is the
dimmer part flowing from
the head, and, as observed
in different comets, it may
be long or short, straight
or curved, single, double,
or multiple. The comet of
1744 had six tails, that of
1823 two. In some comets
the tail is entirely absent.
J Fig. 19. — Donati s Comet (general
Both head and tail are so view).
transparent that all but the faintest stars are easily seen
126 ASTRONOMY.
through them. In 1 858, the bright star Arcturus was seen
through the tail of Donati's comet at a place where the
tail was 90,000 miles in diameter.
292. The number of comets recorded from the earliest
times, beginning with the Chinese annals, to our own is
about 800, but the number observed at present is much
greater than formerly, as many telescopic ones are now
recorded, whereas the old chronicles tell us only of those
in bygone times which were brilliant enough to attract
general attention, and to give rise to the most gloomy
forebodings. It is worthy of remark that in the year of
the Norman invasion, 1066, a fine comet with three tails
appeared, which in the Norman chronicle is given as
evidence of William's divine right to invade this country.
293. We have already stated that these bodies are
probably white-hot masses. N ow when they are far away
from the Sun, their heat is feeble, and their light is
dim, and we observe them in our telescopes as round
misty bodies, moving very slowly, say a few yards in a
second, in the depths of space. Gradually, as the comet
approaches the Sun, and as its motion increases (for, as
we shall see in Chap. IX., the nearer any body, be it
planet or comet, gets to the Sun, the faster it travels), the
Sun's action begins to be felt, the comet gets hotter and
gives out more light, which enables it to become visible
to the naked eye. A violent action commences ; the gas
bursts forth in jets from the coma towards the Sun, and is
instantly driven back again, as the steam of a locomotive
going at great speed is driven back on its path, though
from a different cause. The jets rapidly change their
position and direction, and a tail is formed, which seems
to consist of the smoke or products of combustion driven
off from the coma, or head, probably by the repulsive
power of the Sun, and rendered visible by his light. This
tail is always turned away from the Sun, whether the comet
THE- SOLAR SYSTEM.
127
be approaching or receding from that body. As the comet
still gets nearer the Sun and therefore the Earth, we begin
to see in some instances that the coma or head contains a
kernel or nucleus, which is brighter than the coma itself,
the jets are distinctly visible, and sometimes the coma
consists of a series of envelopes. In the beautiful comet
of 1858 we saw what this meant : the nucleus was con-
tinually throwing off these envelopes or shells which
surrounded it like the layers of an onion, and peeled off,
and these layers expanded outwards, giving place to
others. Seven distinct envelopes were thus seen ; as they
were driven off, they seemed expelled into the tail. Here
we have a reason why the
tails of comets should, as a
rule, increase so rapidly as
they approach the Sun, which
gives rise to all this violent
action : — the tail of the comet
of 1 86 1 was 20,000,000 miles
in length, but this length has
been exceeded in many cases,
notably by the tail of the
comet of 1843, which was
112,000,000 long, the dia-
meter of the coma being
112,000 miles, that of the
nucleus 400 miles.
We have said as a rule,
because Halley's comet, as
observed by Sir John Her-
schel, and Encke's comet,
furnish US with exceptions. Fig. 2o.-Donati's Comet (showing
As these comets approached Head and Envel°Pes)-
the Sun, both tail and coma decreased, and the whole
comet appeared only like a star, Still for all that, in the
128 ASTRONOMY.
majority of instances, comets increase in brilliancy, and
their tails lengthen as they near the Sun, so much so that
in some instances they have been visible in broad day-
light. The enormous effect of a near approach to the
Sun may be gathered from the fact that the comet of
1680 at its perihelion passage, while it was travelling at
the rate of 1,200,000 miles an hour, in two days shot
out a tail 20,000,000 leagues long.
294. In olden times, when less was known about comets,
they caused great alarm — not merely superstitious terror,
which connected their coming with the downfall of a king
or the outbreak of a plague, but a real fear that they would
dash this little planet to pieces should they come into
contact with it. Modern science teaches us that in the
great majority of instances the mass of the comet is so
small that we need not be alarmed ; indeed, there is good
reason to believe that on June 30, 1861, we did actually
pass through the tail of the glorious comet which then
became so suddenly visible to us. There is another fact
too which teaches us the same thing. In 1776, a comet
approached so close to Jupiter that it got entangled among
the satellites of that planet, but the satellites all the time
pursued their courses as if the comet had never existed.
This, however, was by no means the case with the comet ;
it was thrown entirely out of its course, and has changed
its orbit from one with a long period to one with a period
of twenty years or so.
295. There is an instance on record of a comet dividing
itself into two portions, each separate portion afterwards
pursuing distinct but similar orbits. This is Biela's comet,
given in the table in Art. 288. But this is not all. This
twin comet was due back again at the Sun in the end of
January 1866, and it ought to have been visible from the
Earth, as its orbit intersects the orbit of the Earth at the
place occupied by our planet on the 3oth of November,
THE SOLAR SYSTEM. 129
but in spite of the strictest watching nothing was seen of
it. It is believed that, like Lexell's comet, it has been
diverted from its course by some member of our system,
and that in this case the November meteors may have
been the disturbing cause.
296. It has been estimated that there may be many
millions of comets belonging to our system, and perhaps
passing between this and other systems. We see but few
of them, because those only are visible to us which are
well placed for observation when they pass the Earth in
their journey to or from perihelion, while there may be
thousands which at their nearest approach to the Sun are
beyond the orbit of Neptune.
297. In the case of a comet without a nucleus, we have
reason to believe that the coma is a mass of white-hot
gas, similar in composition to that of which the nebulae
are composed ; but we do not yet know that when we
see a bright comet with a nucleus it is composed of similar
material; one thing is certain, that as the tail indicates
the waste, so to speak, of the head, each return to the
Sun must reduce the mass of the comet. A reduction of
speed would in time be enough to reduce the most refrac-
tory comet into a quiet member of the solar family, as the
orbit would become less elliptical, or more circular, at
each return to perihelion. This effect has, in fact, been
observed in some of the short-period comets. Encke's
comet, for instance, now performs its revolution round
the Sun in three days less than it did eighty years ago.
It has been affirmed that this effect is due to the friction
offered by the ethereal medium — an effect we do not per-
ceive in the case of the planets, as their mass is so much
larger — as the resistance of the air stops the flight of a
feather sooner than it does that of a stone. Sir Isaac
Newton has calculated that a,r cubic inch of air at the
Earth's surface — that is, as much as is contained in a
K
130 ASTRONOMY.
good-sized pill-box — if reduced to the density of the air
4,000 miles above the surface, would be sufficient to fill a
sphere the circumference of which would be as large as
the orbit of Neptune. The tail of the largest comet,
if it be gas, may therefore weigh but a few ounces or
pounds ; and the same argument may be applied to the
comet itself, if it be not solid. We can understand, then,
that with such a small supply there is not much room for
waste, and with such a small mass the resistance offered
to it may easily become noticeable.
LESSON XXIV. — LUMINOUS METEORS. SHOOTING
STARS. NOVEMBER SHOWERS. RADIANT POINTS.
298. There are very few nights in the year in which, if
we watch for some time, we shall not see one of those
appearances which are called, according to their brilliancy,
meteors, bolides, or falling or shooting stars. On sortie
nights we may even see a shower of falling stars, and the
shower in certain years is so dense that in some places the
number seen at once equals the apparent number of the
fixed stars seen at a glance :* indeed, it has been calculated
that the average number of meteors which traverse the
atmosphere daily, and which are large enough to be visible
to the naked eye on a dark clear night, is no less than
7,500,000 ; and if we include meteors which would be
visible in a telescope, this number will have to be increased
to 400,000,000 ! so that, in the mean, in each volume as
large as the Earth, of the space which the Earth traverses
in its orbit about the Sun, there are as many as 13,000
small bodies, each body such as would furnish a shooting
* Baxendell.
THE SOLAR SYSTEM. 131
star, visible under favourable circumstances to the naked
eye. If telescopic meteors be counted, this number should
be increased at least forty-fold.
299. It is now generally held that these little bodies are
not scattered uniformly in the space comprised by the
Solar System, but are collected into several groups, some
of which travel like comets, in elliptic orbits round the
Sun ; and that what we call a shower of meteors is due
to the Earth breaking through one of these groups. Two
such groups are well denned, and we break through them
in August and November in each year. The exquisitely
beautiful star-shower which was witnessed during the
year 1866 has placed the truth of this explanation beyond
all doubt. Let us consider how the appearances observed
are connected with the theory, and what the theory actually
is in its details.
300. Here again we must fall back upon our imaginary
ocean (Art. 105) to represent the plane of the ecliptic. Let
us further suppose that the Earth's path is marked out by
buoys placed at every degree of longitude, beginning from
the place occupied by the Earth at the autumnal equinox,
and numbered from right to left from that point. Now
if it were possible to buoy space in this way, we should
see the November group of meteors rising from the
plane at the point occupied by our Earth on the I4th of
November.
301. But why do we not have star-showers every
November? Because the orbit of the meteors has the
principal mass of the little bodies in one part of it, its
extent along the elliptic orbit being such that it requires
two or three years to make its passage round the Sun.
So that to get a star-shower we must not only go through
the orbit, but through that exact part of it where the mass
is collected. Hence we do not go through the group every
year, because the mass of little bodies performs its revolu-
K 2
I32 ASTRONOMY.
tion like a comet, in 33^ years. So that if we go through
the mass one year, it will have passed the node the next
year, and we shall not have a shower again until the mass
happens to be at the node again thirty-three years after.
302. Now what will happen when the Earth, sailing
along in its path, reaches the node and encounters the
mass of meteoric dust, the particles of which travel, as
we know, in the opposite direction ?
303. Let us in imagination connect the Earth and Sun
by a straight line : at any moment the direction of the
Earth's motion will be at right angles to that line (or, as
it is called, a tangent to its orbit) : therefore, as longitudes
are reckoned, as we have seen, from right to left, the
motion will be directed to a point 90° of longitude behind
the Sun. The Sun's longitude at noon on the I4th No-
vember, 1866, was 232° within a few minutes ; 90° from
this gives us 142°.
. 3O4. As therefore the meteors, as we meet them in our
journey, should seem to come from the point of space
towards which the Earth is travelling, and not from any
side street as it were, we ought to see them coming from
a point situated in longitude 142°, or thereabouts. Now
what was actually seen ?
3O5. One of the most salient facts, noticed by those even
who did not see the significance of it, was that all the
meteors seen in the late display really did seem to come
from one part of the sky. In fact, there was a region in
which the meteors appeared trainless, and shone out for
a moment like so many stars, because they were directly
approaching us. Near this spot they were so numerous,
and all so foreshortened, and for the most part faint, that
the sky at times put on almost a phosphorescent appear
ance. As the eye travelled from this region, the trains
became longer, those being longest as a rule which first
made their appearance, over head, or which trended west-
Plate XI.
133
THE SOLAR SYSTEM. 135
ward. Now, if the paths of all had been projected back-
wards, they would have all intersected in one region, and
that region the one in which the most foreshortened ones
were seen. So decidedly did this fact come out, that there
were moments in which the meteors belted the sky like
the meridians on a terrestrial globe, the pole of the globe
being represented by a point in the constellation Leo. In
fact, they all seemed to radiate from that point, and
radiant-point is precisely the name given to it by astro-
nomers. Now the longitude of this point is 142° or
thereabout !
306. The apparent radiation from this point is an effect
of perspective, and hence we gather that the paths of the
meteors are parallel, or nearly so, and that the meteors
themselves are all travelling in straight lines from that
point.
307. Here, then, is proof positive enough that the
meteoric hail was fairly directed against, and as fairly met
by, the Earth. Now here another set of considerations
comes in. Suppose, for instance, we were situated in the
radiant point, and could see exactly the countries which
occupied the hemisphere of our planet facing the meteors,
at the moments our planet entered the shower, when it was
in its midst, and when it emerged again. In consequence
of the Earth's rotation, and as the shower can of course
only fall on the hemisphere of the Earth most forward at
the time, the places at which the shower is central, rising,
and setting, so to speak, will be constantly varying. In
fact, each spectator is carried round by the Earth's rota-
tion, and enters about midnight the front hemisphere of the
Earth — the one which is exposed to the meteoric hail. We
know therefore, again to take an instance from the last
display, that as the shower did not last long into the
morning, the time of maximum for the whole Earth was
certainly not later than that observed at Greenwich ; but
136 ASTRONOMY.
we do not know that it was not considerably earlier. Had
the actual number of meteors encountered by the Earth
remained the same, the apparent number would have
increased from midnight to 6 A.M. ; as at 6 we should have
been nearly in the middle of the front side of the Earth on
which they would be showering.
308. By careful observations of the radiant-point it has
been determined that the orbit of each member of the
November star-shower, and therefore of the whole mass,
is an ellipse with its perihelion lying on the Earth's orbit,
and its aphelion point lying just beyond the orbit of
Uranus ; that its inclination to the plane of the ecliptic
is 17°; and that the direction of the motion of the
meteors is retrograde.
309. Up to the present time 56 such radiant-points,
which possibly indicate 56 other similar groups moving
round the Sun in cometary or planetary orbits, have been
determined. The meteors of particular showers vary in
their distinctive characters, some being larger and brighter
than others, some whiter, some more ruddy than others,
some swifter, and drawing after them more persistent
trains than those of other showers.
LESSON XXV. — LUMINOUS METEORS (continued). CAUSE
OF THE PHENOMENA OF METEORS. ORBITS OF
SHOOTING STARS. DETONATING METEORS. METEOR-
ITES : THEIR CLASSIFICATION. FALLS. CHEMICAL
AND PHYSICAL CONSTITUTION.
31O. Now let us take the case of a single meteor entering
our atmosphere. Why do we get such a brilliant appear-
ance ? In the first place, we have the Earth travelling at
THE SOLAR SYSTEM. 137
the rate of 1,000 miles an hour, plunging into a mass of
bodies whose velocity is at first equal to its own, and is
then increased to 1,200 miles a minute by the Earth's
attraction. The particle then enters our atmosphere at
the rate of 30 miles a second ; its motion is arrested by
the friction of that atmosphere, which puts a break on it,
and as the wheel of a tender gets hot under the same cir-
cumstances, and as a cannon-ball gets hot when the target
impedes its further flight, so does the meteoric particle get
hot. So hot does it get that, at last, as great heat is always
accompanied by light, we see it : it becomes vaporized,
and leaves a train of luminous vapour behind it.
311- It would seem that all the ' particles which com-
pose the November shower are small : it has been esti-
mated that some of them weigh but two grains. They
begin to burn at a height of 74 miles, and are burnt up
and disappear at a height of 54 miles ; the average length
of their visible paths being 42 miles. It is supposed
that the November-shower meteors are composed of more
easily destructible or of more inflammable materials than
aerolitic bodies.
312. What has been said about the appearance of the
November meteors applies to the other star-showers,
notably to the August and April ones, the meteors of
which also travel round the Sun in cometary orbits ; in
fact, there is reason to believe that three bodies, which
were observed and recorded as comets, are really nothing
but meteors, and belong one to the November, one to
the August, and the other to the April group. This dis-
covery, however, is so recent and so unexpected, and so
much has to be done before we can thoroughly under-
stand it, that in this little book it will be sufficient to
state it merely.
313. In the case of the November and August meteors
and shooting-stars generally, the mass is so small that it
133 ASTRONOMY.
is entirely changed into vapour and disappears without
noise. There are other classes of meteoric bodies, how-
ever, with much more striking effects. At times meteors
of great brilliancy are heard to explode with great noise ;
these are called detonating meteors. On Nov. 15, 1859,
a meteor of this class passed over New Jersey ; it was
visible in the full sunlight, and was followed by a series
Fig. 21. — Fire-ball, as observed iy a telescope.
of terrific explosions, which were compared to the dis-
charge of a thousand cannons.* Other meteors are so
large that they reach the Earth before complete vaporiza-
tion takes place, and we then get what is called a fall of
meteoric irons, or meteoric stones, often accompanied
by loud explosions.
314-. Meteorites is the name given to those masses
which, owing to their size, resist the action of the atmo-
sphere, and actually complete their fall to the Earth.
They are divided into aerolites, or meteoric stones;
aerosiderites, or meteoric iron; and aerosiderolite*,
which includes the intervening varieties.
315. We do not know whether these meteors which
occasionally appear, and which are therefore called
* Professor Loomis.
THE SOLAR SYSTEM. 139
sporadic meteors — a term which includes meteors com-
monly so called, bolides, stone-falls, and ironfalls — belong
to group scometic or otherwise, although, like the falling
stars, they affect particular dates ; but, as they are inde-
pendent of geographical position, it has been imagined
that there may be some astronomical and perhaps a
physical difference between them and the ordinary falling
or shooting stars.
316. Among the largest aerolitic falls of modern times
we may mention the following. On April 26, 1803, at
2 P.M. a violent explosion was heard at L'Aigle (in Nor-
mandy) ; and at a distance of eighty miles round, a few
minutes before the explosion was heard, a luminous meteor
with a very rapid motion appeared in the air. Two thou-
sand stones fell, so hot as to burn the hands when touched,
and one person was wounded by a stone upon the arm.
The shower extended over an area nine miles long and
six miles wide, close to one extremity of which the largest
of the stones was found. A similar shower of stones fell
at Stannem, between Vienna and Prague, on the 22d of
May, 1812, when 200 stones fell upon an area eight miles
long by four miles wide. The largest stones in this case
were found, as before, near the northern extremity of
the ellipse. A third stonefall occurred at Orgueil, in the
south of France, on the evening of the I4th of May, 1864.
The area in which the stones were scattered was eighteen
miles long by five miles wide. At Kuyahinza, in Hungary,
on the 9th of June, 1866, a luminous meteor was seen,
and an aerolite weighing six hundredweight, and nearly
one thousand lesser stones, fell on an area measuring ten
miles in length by four miles wide. The large mass was
found, as in the other cases, at one extremity of the oval
area ; the fall was followed by a loud explosion, and a
I -moky streak was visible in the sky for nearly half an hour.*
* Professor Herschel.
140 ASTRONOMY.
317. A chemical examination of these fragments (a
magnificent collection of which is to be seen in the British
Museum) shows that, although in their composition they
are unlike any other natural product, their elements are
all known to us, and that they are all built up of the
same materials, although in each variety some particular
element may predominate. In the main, they are com-
posed of metallic iron and various compounds of silica,
the iron forming as much as 95 per cent, in some cases,
and only I per cent, in others ; hence the three classifica-
tions referred to in Art. 314. The iron is always associated
with a certain quantity of nickel, and sometimes with
cobalt, copper, tin, and chromium. Among the silicates
may be mentioned olivine, a mineral found abundantly
in volcanic rocks, and augite.
318. Besides these substances, a compound of iron,
phosphorus, and nickel, called schreibersite, is generally
found : this compound is unknown in terrestrial che-
mistry. Carbon has also been detected.
319. The chemical elements found in meteorites up to
the present time are as follow : —
Metalloids. Metals.
Oxygen. Iron. Sodium.
Sulphur. Nickel. Cobalt.
Phosphorus. Chromium. Manganese.
Carbon. Tin. Copper.
Silicon. Aluminium. Titanium.
Magnesium. Lead.
Calcium. Lithium.
Potassium. Strontium.
320. Thinking that, unlike terrestrial rocks, meteorites
are probably portions of cosmical matter which has not
been acted on by water or volcanic heat, Mr. Sorby was
led .to study their microscopical structure. He has thus
THE SOLAR SYSTEM. 141
been able to ascertain that the material was at one time
certainly in a state of fusion ; and that the most remote
condition of which we have positive evidence was that
cf small, detached, melted globules, the formation of which
cannot be explained in a satisfactory manner, except by
supposing that their constituents were originally in the
state of vapour, as they now exist in the atmosphere of
the Sun ; and, on the temperature becoming lower, con-
densed into these " ultimate cosmical particles." These
afterwards collected together into larger masses, which
have been variously changed by subsequent metamorphic
action, and broken up by repeated mutual impact, and
often again collected together and solidified. The meteoric
irons are probably those portions of the metallic con-
stituents which were separated from the rest by fusion
when the nietamorphism was carried to that extreme
point.
CHAPTER IV.
APPARENT MOVEMENTS OF THE HEAVENLY
BODIES.
LESSON XXVI.— THE EARTH A MOVING OBSERVA-
TORY. THE CELESTIAL SPHERE. EFFECTS OF THE
EARTH'S ROTATION UPON THE APPARENT MOVE-
MENTS OF THE STARS. DEFINITIONS.
321. IN the previous chapters we have studied in turn
the whole universe, of which we form a part ; the nebulae
and stars of which it is composed ; the nearest star to us
— the Sun ; and lastly, the system of bodies which centre
in this star, our own Earth being among them.
We should be now, therefore, in a position to see exactly
what "the Earth's place in Nature" — what its relative
importance — really is. We find it, in fact, to be a small
planet travelling round a small star, and that the whole
solar system is but a mere speck in the universe — an
atom of sand on the shore, a drop in the infinite ocean of
space.
322. But, however small or unimportant the Earth
may be compared to the universe generally, or even to the
Sun, it is all in all to us inhabitants of it, and especially
so from an astronomical point of view ; for although in
what has been gone through before, we have in imagination
A P PARE NT MO VEMENTS. 143
looked at the various celestial bodies from all points of
view, our bodily eyes are chained to the Earth — the Earth
is, in fact, our Observatory, the very centre of the visible
creation ; and this is why, until men knew better, it was
thought to be the very centre of the actual one.
323. More than this, the Earth is not a fixed observa-
tory ; it is a moveable one, and, as we know, has a double
movement, turning round its own axis while it travels
round the Sun. Hence, although the stars and the Sun
are at rest, they appear to us, as every child knows, to
have a rapid movement, and rise and set every twenty-
four hours. Although the planets go round the Sun, their
circular movements are not visible to us as such, for our
own annual movement is mixed up with them
Having described the heavens then as they are, we must
describe them as they seem. The real movements must
now give way to the apparent ones; we must, in short,
take the motion of our observatory, the Earth, into
account.
324. To make this matter quite clear, before we pro-
ceed, let the Earth be supposed to be at rest : neither
turning round on its own axis, nor travelling round the
Sun. What would happen is clearly this — that the side
of it turned towards the Sun would have a perpetual day,
the other side of it perpetual night. On one side the
Sun would appear at rest — there would be no rising and
setting ; on the other side the stars would be seen at rest
in the same manner : the whole heavens would be, as it
were, dead.
325. Again, let us suppose the Earth to go round the
Sun as the Moon goes round the Earth, turning once on
its axis each revolution, which would result in the same
side of the Earth always being turned towards the Sun.
The inhabitants of the lit-up hemisphere would, as before,
see the Sun motionless in the heavens; but in this case,
144 ASTRONOMY.
those on the other side, although they would never see
the Sun, would still see the stars rise and set once a year.
These examples should give you an idea of the way in
which the various apparent movements of the heavenly
bodies are moulded by the Earth's real movements, and
we shall find that the former are mainly of two kinds —
daily apparent movements, and yearly apparent move-
ments, which are due, the first to the Earth's daily rotation,
or turning on its axis, and the second to the Earth's yearly
revolution or journey round the Sun. In each case the
apparent movement is, as it were, a reflection of the real
one, and in the opposite direction to the real one ; exactly,
what we observe when we travel smoothly in a train or
balloon. When we travel in an express train, the objects
appear to fly past us in the opposite direction to that in
which we are going ; and in a balloon, in which not the
least sensation of motion is felt; to the occupant of the
car it is always the Earth which appears to fall down
from it, and rush up to meet it, while the balloon itself
rises or descends.
326. We will first study the effects of the Earth's
rotation on the apparent movements of the stars. The
daily motion of the Earth is very different in different
parts — at the equator and at a pole, for instance. An
observer at a pole is simply turned round without changing
his place, while one at the equator is swung round a
distance of 24,000 miles every day. We ought, therefore,
to expect to see corresponding differences in the apparent
motions of the heavens, if they are really due to the actual
motions of our planet. Now this is exactly what is ob-
served, not only is the apparent motion of the heavens
from east to west — the real motion of the Earth being from
west to east — but those parts of the heavens which ai
over the poles appear at rest, while those over the equatoj
appear in most rapid motion. In short, the apparent motioi
A PPA RENT MO VEMENTS. 145
of the celestial sphere — the name given to the apparent
vault of the sky — to which the stars appear to be fixed,
and to which, in fact, their positions are always referred,
is exactly similar to the real motion of the terrestrial
one, our Earth ; but, as we said before, in an opposite
direction.
327- Before we proceed further, however, * we must
say something more about this celestial sphere, and ex-
plain the terms employed to point out the different parts
of it.
328. In the first place, as the stars are so far off, we
may imagine the centre of the sphere to lie either at the
centre of the Earth or in our eye, and we may imagine it
as large or as small as we please. The points where the
terrestrial poles would pierce this sphere, if they were long
enough, we shall call the celestial poles 3 the great circle
lying in the same plane as the terrestrial equator we shall
call the celestial equator, or equinoctial ; the point over-
head the zeuithj the point beneath our feet the nadir.
Now, as the whole Earth is belted by parallels of
latitude and meridians of longittide, so are the heavens
belted to the astronomer with parallels of declination and
meridians of right ascension. If we suppose the plane in
which our equator lies extended to the stars, it will pass
through all the points which have no declination (o°).
Above and below we have north and south declination,
as we have north and south latitude, till we reach the
pole of the equator (90°). As we start from the meri-
dian of Greenwich in the measure of longitude -, so do we
start from a certain point in the celestial equator occupied
by the Sun at the vernal equinox, called the first point
of Aries, in the measure of right ascension. As we say
such a place is so many degrees east of Greenwich, so we
say such a star is so many hours, minutes, or seconds
east of the first point of Aries.
L
146 ASTRONOMY.
329. In short, as we define the position of a place on
the Earth by saying that its latitude and longitude (in
degrees) are so-and-so, so do we define the position of a
heavenly body by saying that, referred to the celestial
sphere, its declination (in degrees) and right ascension
(in time reckoned from Aries) are so-and-so.
Sometimes the distance from the north celestial pole is
given instead of that from the celestial equator. This
is called north-polar distance.
These terms apply to the celestial sphere generally.
When we consider that portion of it visible in any one
place, or the sphere of observation, there are other
terms employed, which we will state in continuation.
In any place the visible portion of the celestial sphere
seems to rest either on the Earth or sea. The line where
the heavens and Earth seem to meet is called the visible
horizon; the plane of the visible horizon meets
the Earth at the spectator. The rational, or true
horizon, is a great circle of the heavens, the plane of
which is parallel to the former plane, but which, instead
of passing through the spectator, passes through the
centre of the Earth. A vertical line is a line passing
from the zenith to the nadir, and therefore through the
spectator ; and therefore, again, it is at right angles to
the planes of the horizon, or upright with respect to them.
If it is desired to point out the position of a heavenly
body not on the celestial sphere generally, but on that
portion of it visible on the horizon of a place at a given
moment of time, this is done by determining either its
altitude or its zenith distance, and its azimuth (instead
of its declination and right ascension).
Altitude is the angular height above the horizon.
Zenith-distance is the angular distance from the zenit]
Azimuth is the angular distance between two planes
one of which passes through the north or south point
APPARENT MOVEMENTS. 147
(according to the hemisphere in which the observation
is made), and the other through the object, both passing
through the zenith.
The celestial meridian of any place is the great circle
on the sphere corresponding to the terrestrial meridian
of that place, cutting therefore the north and south points.
The prime vertical is another great circle passing
through the east and west points and the zenith.
LESSON XXVII. -- APPARENT MOTIONS OF THE
HEAVENS, AS SEEN FROM DIFFERENT PARTS OF
THE EARTH. PARALLEL, RIGHT, AND OBLIQUE
SPHERES. CIRCUMPOLAR STARS. EQUATORIAL
STARS, AND STARS INVISIBLE IN THE LATITUDE
OF LONDON. USE OF THE GLOBES.
33O. We are now in a position to proceed with our in-
quiry into the apparent movement of the celestial sphere.
In what follows we shall continue to talk of the Sun or a
star rising or setting, although the reader now understands
that it is, in fact, the plane of the observer's horizon which
changes its direction with regard to the heavenly body, in
consequence of its being carried round by the Earth's
motion. When a star is so situated that it is just visible
on the eastern horizon, the star is said to rise ; when the
rotation of the Earth has brought the plane of the horizon
under the meridian which passes through the star, it is
said to culminate or pass the meridian, or transit ; and
when the plane of the horizon is carried to the nadir of
the point it occupied when it rose to the star, the star
appears on the opposite — that is, the western horizon, and
is said to set.
L 2
I48
ASTRONOMY.
331. Let Fig. 22 represent our imaginary celestial
sphere, and N. an observer at the north pole of the Earth.
Fig. 22. — The Celestial Sphere, as viewed I'roiu the Po!e.v A Parallel sphere.
To him the north pole of the heavens and the zenith
coincide, and his true horizon is the celestial cquatoi.
Fig. 23. — The Celestial Sphere, a* viewcu iioiu the Equator. A Right sphere.
Above his head is the pivot on which the heavens
appear to revolve, as underneath his feet is the pivot on
A PPA RENT MO VEMENTS.
149
which the Earth actually revolves ; and round this point
the stars appear to move in circles, the circles getting
larger and larger as the horizon is approached. The
stars never rise or set, but always keep the same distance
from the horizon. The observer is merely carried
round by the Earth's rotation, and the stars
seem carried round in the opposite direction.
Fig. 24. — The Celestial Sphere, viewed from a middle latitude. An Oblique
sphere. In this woodcut Dl)' shows the apparent path of a circumpolar
star ; B & B" the path and rising and setting points of an equatorial star ;
CC'C" and A A A" those of stars of mid-declination, one north and the
other south.
332. We will now change our position. In Fig. 23
the celestial sphere is again represented, but this time we
suppose an observer, Q, at its centre, to be on the Earth's
equator. In this position we find the celestial equator in
the zenith, and the celestial poles PP on the true horizon,
and the stars, instead of revolving round a fixed point
overhead, and never rising or setting, rise and set every
150 ASTRONOMY.
twelve hours, travelling straight up and down along circles
which get smaller and smaller as we leave the zenith and
approach the poles. The spectator is carried up
and down by the Earth's rotation, and the stars
appear to be so carried. Yet another figure, to
show what happens half-way between the poles and the
equator At O, in Fig. 24, we imagine an observer to be
placed on our Earth, in lat. 45° (that is, half-way between
the equator in lat. o°, and the north pole in lat. 90°). Here
the north celestial pole will be half-way between the zenith
and the horizon (see Figs. 22 and 23); and close to the
pole he will see the stars describing circles, inclined,
however, and not retaining the same distance from the
horizon. As the eye leaves the pole, the stars rise and set
obliquely, describe larger circles, gradually dipping more
and more under the horizon, until, when the celestial
equator, B B' B" , is reached, half their journey is per-
formed below it. Still going south, we find the stars
rising less and less above the horizon, until, as there were
northern stars that never dip below the horizon, so there
are southern stars which never appear above it.
333. In lat. 45° south, the southern celestial pole would
in like manner be visible ; the stars we never see in the
northern hemisphere never set; the stars which never set
with us, never rise there ; the stars which rise and set
with us set and rise with them.
334 Now it is evident that if we divide the celestial
sphere into two hemispheres, northern and southern, an
observer at the north pole sees the northern stars only ;
one at the south pole the southern stars only ; while one
at the equator sees both north and south stars. An
observer in a middle north latitude sees all the northern
stars and some of the southern ones ; and another in a
middle southern latitude sees all the southern stars and
some of the northern ones.
I
APPARENT 'MO VEMENTS. 1 5 1
335. Hence, in middle latitudes, and therefore in
England, we may divide the stars into three classes : —
I. Those northern stars which never set (northern
circumpolar stars).
II. Those southern stars which never rise (southern
circumpolar stars).
III. Those stars which both rise and set.
336. It is easily gathered from Figs. 22 — 24 that the
height of the celestial pole above the horizon at any place
is equal to the latitude of that place ; for at the equator, in
lat. o°, the pole was on the horizon, and consequently its
altitude was nothing ; at the pole in lat. 90° it was in
the zenith and its altitude was consequently 90°; while
in lat. 45° its altitude was 45°. In London, therefore, in
lat. 51^°, its altitude will be 51^°, and hence stars of less
than that distance from the pole will always be visible,
as they will be above the horizon when passing below the
pole. All the stars, therefore, within 51° of the north pole
will form Class I.; all those within 51° of the south pole
Class II.; and the remainder — that is, all stars from lat.
39° N. (90°— 5i° = 39°) to 39° S.— will form Class III.
337. In these and similar inquiries the use of the ter-
restrial and celestial globes is of great importance in
clearing our ideas.
To use either properly we must begin by making each
a counterpart of what is represented — that is, the north
pole must be north, the south pole south, and moreover
the axis of either globe must be made parallel with the
Earth's axis.
338. This is accomplished generally by the use of a
compass, the indication of that instrument being cor-
rected by its known variation. This variation at present
is about 21° to the west of the true north ; therefore the
true north lies 21° to the east of magnetic north, and the
152
ASTRONOMY.
brazen merid.an of the globe must be placed accordingly.
Secondly, the wooden horizon of the globe must be level;
it will then represent the horizon of the place.
339. This done, the pole — the north pole in our case-
must be elevated to correspond with the latitude of the
APPARENT MOVEMENTS.
'55
place where the globe is used. At the poles this would
be 90°, at the equator o°, and at London 51^°.
34O. If we then turn the terrestrial globe from west to
east, we shall exactly represent the lie, and the direction
of motion of the Earth. If we then turn the celestial
154 ASTRONOMY.
globe from east to west, we shall exactly represent the
apparent motions of the heavens to a spectator on the
Earth supposed to occupy the centre of the globe, as in
Figs. 22-24. The wooden horizon will represent the true
horizon ; and why some stars never set and others never
rise in these latitudes, will at once be apparent.
34-1. At the present time the northern celestial pole
lies in Ursa Minor, and a star in that constellation very
nearly marks the position of the pole, and is therefore
called polari*, or the pole-star. We shall see further on
(LessonXLIII.),that the direction in which the Earth's axis
points is not always the same, although it varies so slowly
that a few years do not make much difference. As a con-
sequence, the position of the celestial pole, which is defined
by the Earth's axis prolonged in imagination to the stars,
varies also. One of the most striking circumpolar con-
stellations is Ursa Major (the Great Bear), the Plough,
or Charles' Wain, as it is otherwise called. Two stars
in this are called the pointers, as they point to the pole-
star, and enable us at all times to find it easily.
The other more important circumpolar constellations
are Cassiopea, Cepheus, Cygnus, Draco, Auriga (the
brightest star of which, Capella, is very near the horizon
when below the pole), and Perseus. The principal
southern circumpolar constellations which never rise in
this country, are Crux, Centaurus, Argo, Ara, Lepus,
Eridanus, and Dorado. Nearly all the other constel-
lations mentioned in Arts. 37-39 belong to Class III.
342. If, then, we would watch the heavens on a clear
night from hour to hour, to get an idea of these apparent
motions, we may best accomplish this either by looking
eastward to see the stars rise, westward to see them set,
northward to the pole to watch the circular movement
round that point. If, for instance, we observe the Great
Bear, we shall see it in six hours advance from one
APPARENT MOVEMENTS.
155
of its positions shown in the accompanying figure, to
the next.
343. As the Earth's rotation is accomplished in
23 h. 54m. 565., it follows that the apparent movement of
the celestial sphere is completed in that time; and were
there no clouds, and no Sun to put the stars out in the
day-time — eclipsing them by his superior brightness — we
Fig. 27. — The Constellation of the Great Bear, in four different positions,
after intervals of 6 hours, showing the effect of the apparent revolution of
the celestial sphere upon circumpolar stars.
should see the grand procession of distant worlds ever
defiling before us, and commencing afresh after that
period of time.
This leads us to the effect of the Earth's yearly journey
round the Sun upon the apparent movement of the
stars.
156 ASTRONOMY.
LESSON XXVI 1 1.— POSITION OF THE STARS SEEN AT
MIDNIGHT. DEPENDS UPON THE TWO MOTIONS OF
THE EARTH. How TO TELL THE STARS. CELESTIAL
GLOBE. STAR-IMAPS. THE EQUATORIAL CONSTEL-
LATIONS. METHOD OF ALIGNMENTS.
344*. We see stars only at night, because in the day-
time the Sun puts them out ; consequently the stars we see
on any night are the stars which occupy that half of the
celestial sphere opposite to the point in it occupied at that
time by the Sun. We have due south, at midnight, the
very stars which occupy the celestial meridian 1 80° from
the Sun's place, as the Sun, if it were not below the horizon
in England, would be seen due north.
34-5. Now as we go round the Sun, we are at different
times on different sides, so to speak, of the Sun ; and if
we could see the stars beyond him, w.e should see them
change ; but what we cannot do at mid-day, in conse-
quence of the Sun's brightness, we can easily do at mid-
night; for if the stars behind the Sun change, the stars
exactly opposite to his apparent place will change too,
and these we can see in the south at midnight.
34-6. It is clear, in fact, that in one complete revolution
of the Earth round the Sun every portion of the visible
celestial sphere will in turn be exposed to view in the
south at midnight ; and as the revolution is completed in
365 days, and there are 360° in a great circle of the
sphere, we may say broadly that the portion of the
heavens visible in the south at midnight advances i°
from night to night, which 1° is passed over in 4 minute
as the whole 360° are passed over in nearly 24 hours.
APPARENT MOVEMENTS. 157
347. This advance is a consequence of the difference
between the lengths of the day as measured by the fixed
stars and by the moving Sun, as we shall explain presently.
We may here say, that as the solar day is longer than the
sidereal one, the stars by which the latter is measured
gain upon the solar day at the rate we have seen ; so that,
as seen at the same hour on successive nights, the whole
celestial vault advances to the westward, the change due
to one month's apparent yearly motion being equal to
that brought about in two hours by the apparent daily
motion.
34-8. Hence the stars south at midnight (or opposite
the Sun's place) on any night, were south at 2A.M. a month
previously, and so on; and will be south a month hence
at 10 o'clock P.M., and so on.
349. The best way to obtain a knowledge of the various
constellations and stars is to employ a celestial globe.
We first, as seen in Arts. 337-9, place its brass meridian
in the plane of the meridian of the place in which the
globe is used, and make the axis of the globe parallel to
the axis of the Earth, and therefore of the heavens, by
elevating the north pole (in our case) until its height
above the wooden horizon is equal to the latitude of the
place. We next bring under the brazen meridian the
actual place in the heavens occupied by the Sun at the
time ; this place is given for every day in the almanacs.
We thus represent exactly the position of the heavens at
mid-day, by bringing the Sun's place to the brazen me-
ridian, and the index is then set at 1 2. The reason for
this is obvious ; it is always 12, or noon, at a place when
the Sun is in the meridian of that place. We then, if the
time at the place is after noon, move the globe on till the
index and the time correspond ; if the time is before noon,
we move the globe back — that is, from east to west, till
the index and time correspond in like manner.
158 ASTRONOMY.
35 o. When the globe has been rectified, as it is called,
in this manner, we have the constellations which are
rising on the eastern horizon, just appearing above the
eastern part of the wooden horizon. Those setting are
similarly near the western part of the wooden horizon.
The constellations in the zenith at the time will occupy
the highest part of the globe, while the constellations
actually on the meridian will be underneath the brazen
meridian of the globe.
351. Further, it is easy at once to see at what time any
stars will rise, culminate, or set, when the globe is rectified
in this manner. All that is necessary is, as before, to
bring the Sun's place, given in the almanac, to the
meridian, and set the index to 12. To find the time at
which any star rises, we bring it to the eastern edge of
the wooden horizon, and note the time, which is the time
of rising. To find the time at which any star sets, we
bring it similarly to the western edge of the wooden
horizon and note the time, which. is the time of setting.
To find the time at which any star culminates, or passes
the meridian, we bring the star under the brass meridian
and note the time, which is the time of meridian passage.
352. In the absence of the celestial globe, some such
table as the following is necessary, in which are given the
positions occupied by the constellations at stated hours
during each month in the year. When the positions of
the constellations are thus known, some star-maps (the
small ones published by the Society for Promoting Useful
Knowledge are amply sufficient) should be referred to, in
which various bright stars which go to form each constel-
lation should be well studied ; the constellation should
then be looked for in the position indicated by the table,
in the sky itself. When any constellation is thus recog-
nised, the star-map should again be studied, in order that
the stars in its vicinity may next be traced.
A PPA RENT MO VEMENTS. 1 59
CONSTELLATIONS VISIBLE IN THE LATITUDE OF
LONDON THROUGHOUT THE YEAR.*
JAN. 20, 10 P.M. (Feb. 19, 8 P.M.; Dec. 21, midnight).
N — S. Draco, polaris, * Auriga, Orion, Canis Major.
E — W. Leo, Lynx, * Perseus, Pisces.
NE — SW. Bootes, Ursa Major,* Taurus, Eridanus.
SE — N W. Hydra, Gemini, * Cassiopea, Cygnus.
FEB. 19, 10 P.M. (March 21, 8 P.M.; Jan. 20, midnight).
N — S. Cygnus, Draco, polaris, *Lynx, Gemini, Canis
Minor.
E — W. Virgo, Coma Berenicis, Ursa Major, * Auriga,
Argo, Taurus, Aries.
NE — SW. Corona Borealis, Ursa Major, * Orion, Eri-
danus.
SE — NW. Leo, * Cassiopea, Andromeda.
MARCH 21, IOP.M. (April 20, 8 P.M.; Feb. 19, midnight).
N — S. Cepheus, polaris, *Ursa Major, Leo Minor,
Leo, Hydra.
E— W. Serpens, Bootes, * Taurus.
NE — SW. Hercules, Draco, * Cancer, Canis Minor,
Canis Major.
SE — NW. Virgo, Leo, * Cameleopardalis, Perseus.
APRIL 20, 10 P.M. (May 21, 8 P.M.; March 21, midnight).
N — S. Cassiopea, Cepheus, polaris, *Ursa Major,
Coma Berenicis, Virgo, Corvus.
* The asterisk placed in the line denotes that the zenith separates the two
constellations between which the asterisk is placed. When the asterisk is
prefixed to any constellation, the constellation itself occupies the zenith.
160 ASTRONOMY.
E — W. Ophiuchus, Hercules, Corona Borealis, Bootes,
* Gemini.
NE — SW. Cygnus, Draco, * Leo, a Hydrce.
SE — NW. Libra, Bootes, * Auriga, Perseus.
MAY 21, 10 P.M. (June 21, 8 P.M.; April 20, midnight).
N — S. Cassiopea, polaris, *rj Ursa Major is, Arc-
turus (in Bootes).
E — W. Aquila, Lyra, Hercules, * Ursa Major, Leo
Minor, Cancer.
NE — SW. Cygnus, Draco, * Canes Venatici, Coma
Berenicis, ft Lconis.
SE — NW. Ophiucus, Serpens, Bootes, * Ursa Major,
Lynx, Auriga.
JUNE 21, 10 P.M. (July 22, 8 P.M.; May 21, midnight).
N— S. Perseus, Cameleopardalis, polaris, * Draco,
Hercules, Corona Borealis, Serpens, Scorpio.
E — W. f Pegasi, Cygnus, Lyra, * q Ursa Majoris,
Canes Venatici, Leo.
NE— SW. a Andromeda, Cepheus, * Bootes, Virgo.
SE — NW. Sagittarius, Aquila, Hercules,* Ursa Major,
Gemini.
JULY 22, TO P.M. (Aug. 23, 8 P.M.; June 21, midnight).
N — S. Auriga, Cameleopardalis, polaris, * Draco,
Hercules, Sagittarius.
E — W. Pegasus, Cygnus, * Bootes, Virgo.
NE — SW. Andromeda, Cassiopea, Cepheus, * Hercules.
Serpens, Libra.
SE — NW. Capricornus, Aquila, Lyra, * Ursa Major, Leo
Minor.
A P PARE NT M O VEMENTS. \ 6 1
AUG. 23, 10 P.M. (Sept. 23, 8 P.M.; July 22, midnight).
N — S. Lynx, polaris, Draco, *Cygnus, Vulpecula,
Aquila, Capricornus.
E — W. Pisces, a Andromeda, * Draco, Hercules, Co-
rona Borealis, Bootes.
NE— SW. Perseus, Cassiopea, Cepheus, * Lyra, Ophiu-
chus.
SE — NW. Aquarius, Pegasus, * Draco, Ursa Major.
SEPT. 23, 10 P.M. (Oct. 23, 8 P.M.; Aug. 23, midnight).
N — S. Ursa Major, polaris, * Lacerta, Pegasus,
Aquarius, Piscis Australis.
E — W. Aries, Andromeda, * Cygnus, Lyra, Hercules.
.NE — SW. Auriga, Cassiopea, * Cygnus, Aquila.
SE — NW. Cetus, Pisces, a Andromeda, * Draco, Bootes.
OCT. 23, 10 P.M. (Nov. 22, 8 P.M.; Sept. 23, midnight).
N — S. Ursa Major, polaris, * Cassiopea, Andromeda,
y Pegasi, Pisces, Cetus.
E — W. Orion, Taurus, Perseus, * Cygnus, Aquila.
NE— SW. Lynx, Cameleopardalis, * Pegasus, Capri-
cornus.
SE— NW. Eridanus, Cetus, Aries, Andromeda,* Ce-
pheus, # Draconis, Hercules.
Nov. 22, 10 P.M. (Dec. 21, 8P.M.; Oct. 23, -midnight).
N — S. T) Ursa Majoris, Draco, polaris, * Perseus,
Triangula, Aries, Cetus.
E — W. Canis Minor, Gemini. Auriga, * Lacerta, Del-
phinus, Aquila.
NE — SW. Leo Minor, Cameleopardalis, * Andromeda,
@ Pegasi, Aquarius.
SE — NW. Lepus, Orion, Taurus, * Cassiopea, Cepheus,
Lyra.
M
1 62
ASTRONOMY.
DEC. 21, 10 P.M. (Jan. 20, 8 P.M.; Nov. 22, midnight).
N— S. Hercules, Draco, polaris, *Perseus, Taurus.
Eridanus.
E — W. Leo, Gemini, Auriga, * Andromeda, Pegasus.
NE— SW. Ursa Major, * Aries, Cetus.
SE— NW. Canis Major, Orion, Taurus, * Cassiopea.
Cepheus, Cygnus.
A ri' A RENT
353. In Fig. 26 some of the circumpolar constellation?
nave already been represented. In Fig. 28 are given
some of the constellations in the equatorial zone visible
on Jan. 2oth to the south.
The central constellation is Orion, one of the most
marked in the heavens ; when all the bright stars in this
M 2
164
ASTRONOMY.
asterism arc known, many of the surrounding ones
may easily be found, by means of alignments. For in-
stance, the line formed by the three stars in the belt, if
produced eastward, will pass near Sirius, the brightest
star in the northern heavens.
APPARENT MO VEMENTS. 165
35-4. Fig. 29 represents in like manner the appearance
of the heavens a little south of the zenith in May : the
bright star Arcturus (a Bootis) being then neaily on the
meridian. The constellation Hercules is easily recognised
by means of the trapezium formed by four of its stars.
355. In Fig. 30 the square of Pegasus is a very marked
object, and this once recognised in the sky, may, by
means of star-maps, be made the start-point of many new
alignments.
356. The first magnitude stars should be first known ;
then the second ; and so on till the positions of all the
brighter ones in the different constellations are impressed
upon the memory — no difficult task after a little practice,
and comparison of the sky itself with good small maps.
LESSON XXIX.— APPARENT MOTION OF THE SUN.
DIFFERENCE IN LENGTH BETWEEN THE SIDEREAL
AND SOLAR DAY. CELESTIAL LATITUDE AND
LONGITUDE. THE SIGNS OF THE ZODIAC. SUN'S
APPARENT PATH. How THE TIMES OF SUNRISE
AND SUNSET, AND THE LENGTH OF THE DAY AND
NIGHT, MAY BE DETERMINED BY MEANS OF THK
CELESTIAL GLOBE.
357. The efTect of the Earth's daily movement upon
the Sun is precisely similar to its efTect upon the stars ;
that is, the Sun appears to rise and set every day ; but in
consequence of the Earth's yearly motion round it, it
appears to revolve round the Earth more slowly than
the stars ; and it is to this that we owe the difference
between star-time and sun-time, or, in other words be-
tween the lengths of the sidereal and solar day.
1 66 ASTRONOMY.
358. How this difference arises is shown in Fig. 31,
in which are seen the Sun, and the Earth in two posi-
tions in its orbit, separated by the time of a complete
rotation. In the first position of the Earth are shown one
observer, a, with the Sun on his me.Llian, and another, b,
with a stir on his: the two observers being exactly on
opposite sides of the Earth,
and in a line drawn through
the centres of the Earth and
Sun. In the second position,
when the same star comes to
<£'s meridian, a sees the Sun
still to the east of his, and
he must be carried by the
Earth's rotation to c before
the Sun occupies the same
apparent position in the hea-
vens it formerly did — that is.
before the bun is again in
his meridian. The solar day,
therefore, will be longer than
the sidereal one by the time
it takes a to travel this dis-
tance.
Of course, were the Earth
//V. 31. — Diagram Jioxylng how at rest tnjs difference COllUl
the difference between the lengths
of the Sidereal and Mean day HOt have anseil, and the Solar
arises- day is a result of the Earth's
motion in its orbit, combined with its rotation.
359. Moreover, the Earth's motion in its orbit is not
uniform, as we shall see subsequently ; and, as a conse-
quence, the apparent motion of the Sun is not uniform,
and solar days are not of the same length ; for it is evident
that if the Earth sometimes travels faster, and therefore
further, in the interval of one rotation than it does at
APPARENT MOVEMENTS. 167
others, the observer a has further to travel before he gets
to c\ and as the Earth's rotative movement is uniform, he
requires more time. In a subsequent chapter it will be
shown how this irregularity in the apparent motion of the
Sun is obviated.
360. The apparent yearly motion of the Sun is so
important that astronomers map out the celestial sphere
by a second method, in order to indicate his motion more
easily ; for as the plane of the celestial equator, like the
plane of the terrestrial equator, does not coincide with the
plane of the ecliptic, the Sun's distance from the celestial
equator varies every minute. To get over this difficulty,
they make of the plane of the ecliptic a sort of second
celestial equator. They apply the term celestial latitude
to angular distances from it to the poles of the heavens,
which are 90° from it north and south. They apply
the term celestial longitude to the angular distance —
reckoned on the plane of the ecliptic — from the position
occupied by the Sun at the vernal equinox, reckoning
from left to right up to 360°. This latitude and longitude
may be either heliocentric or geocentric, — that is,
reckoned from the centre either of the Sun or Earth
respectively.
361. The celestial equator in this second arrangement
is represented by a circle called the aodiac, which is not
only divided, like all other circles, into degrees, &c., but
into signs of 30° each. These, with their symbols, are as
follow : —
Spring Signs. Summer Signs. Autumn Signs. Winter Signs.
T Aries. ** Cancer. — Libra. ^ Capricorn,
tt Taurus. $ Leo. TO Scorpio. *& Aquarius,
n Gemini. *n Virgo. t Sagittarius. * Pisces.
At the time these signs were adopted the Sun entered
the constellation Aries at the vernal equinox, and occupied
168 ASTRONOMY.
in succession the constellations bearing the same names ;
but at present, owing to the precession of the equinoxes,
which we shall explain subsequently, the signs no
longer correspond with the constellations, which
must therefore not be confounded with them.
362. Now it follows, that, as these two methods of di-
viding the celestial sphere, and of referring the places of
the heavenly bodies to it, are built, as it were, one on the
plane of the terrestrial equator, and the other on the
plane of the ecliptic, (i) the angle formed by the celestial
equator with the plane of the ecliptic is the same as that
formed by the terrestrial one, — that is, 23^° nearly ; and
(2) the poles of the heavens are each the same distance,
— that is, 23^°, from the celestial poles.
Moreover, if we regard the centre of the celestial sphere
as lying at the centre of the Earth, it is clear that the
two planes will intersect each other at that point, and that
half of the ecliptic will be north of the celestial equator
and half below it ; and there will be two points opposite
to each other at which the ecliptic will cross the celestial
equator.
363. Now as the Sun keeps to the ecliptic, it follows
that at different parts of its path it will cross the celestial
equator, be north of it, cross it again, and be south of it,
and so on again ; in other words, its latitude remaining
the same, its declination or distance from the celestial
equator will change.
364-. Hence it is, that although the Sun rises and sets
every day, its daily path is sometimes high, sometimes
low. At the vernal equinox, — that is, when it occupies
one of the points in which the zodiac cuts the equator, — it
rises due east, and sets due west, like an equatorial star ;
then gradually increasing its north declination, its daily
path approaches the zenith, and its rising and setting
points advance northwards, until it occupies the part of
APPARENT MO VEMENTS. 1 69
the zodiac at which the planes of the ecliptic and equator
are most widely separated. Here it appears to stand
still ; we have the summer solstice (sol, the sun, and stare,
to stand), and its daily path is similar to that of a star of
23-!* north declination. It then descends again through
the autumnal equinox to the winter solstice, when its
apparent path is similar to that of a star of 23^° south
declination, and its rising and setting points are low
down southward.
365. The use of the celestial globe is very important
in rendering easily understood many points connected
with the Sun's apparent motion. Having rectified the
globe, as directed in Arts. 337-9 and 349, the top of the
globe will represent the zenith of London, a miniature
terrestrial globe, with its axis parallel to the celestial
one, being supposed to occupy the centre of the latter.
By bringing different parts of the ecliptic to the brass
meridian, the varying meridian height of the Sun, on
which the seasons depend (Lesson XIII.), is at once
shown.
366. In addition to this, if we find from the almanac
the position of the Sun in the ecliptic on any day, and
bring it to the brass meridian, the globe represents the
positions of the Sun and stars at noonday ; we may,
however, neglect the stars. The index-hand is, therefore,
set to 12. If the globe be perfectly rectified, and we turn
it westward till the Sun's place is close to the wooden
horizon, the globe then represents sunset, and the index
will indicate the time of sunset. If, on the other hand,
we turn the Sun's place eastward from the brass meridian
till it is close to the eastern edge of the wooden horizon,
the globe represents in this case sunrise, and the index
will indicate the time of sunrise.
367. If the path of the Sun's place when the globe is
turned from the point occupied at sunrise to the point
I7o ASTRONOMY.
occupied at sunset be carefully followed with reference
to the horizon, the diurnal arc described by the Sun at
different times of the year will be shown.
368. It is clear, that at noon and midnight the Sun is
mid-way between the eastern and western parts of the
horizon — one part of the diurnal arc being above the
horizon, the other below it. The time occupied, there-
fore, from noon to sunset is the same as from sunrise to
noon. Similarly, the time from midnight to sunrise is
equal to that from sunset to midnight.
369. As civil time divides the twenty-four hours into
two portions, reckoned from midnight and noon, we have
therefore a convenient method of learning the length of
the day and night from the times of sunrise and sunset.
For instance, if the Sun rises at 7, the time from midnight
to sunrise is seven hours ; but this time is equal, as has
been seen, to the time from sunset to midnight, therefore
the night is fourteen hours long. Similarly, if the Sun sets
at 8, the day is twice eight, or sixteen hours long. So
that — Double the time of the Sun's setting gives the
length of the day.
Double the time of the Sun's rising gives the length
of the night.
LESSON XXX.— APPARENT MOTIONS OF THE MOON
AND PLANETS. EXTREME MERIDIAN HEIGHTS OF
THE MOON : ANGLE OF HER PATH WITH THE
HORIZON AT DIFFERENT TIMES. HARVEST MOON.
VARYING DISTANCES, AND VARYING APPARENT SIZE
OF THE PLANETS. CONJUNCTION AND OPPOSITION.
37O. The Moon, we know, makes the circuit of the
Earth in a lunar month, — that is, in 29.} days ; in one
A PPA REN T MO VEMENTS. 1 7 1
day, therefore, she will travel, supposing her motion to be
uniform, eastward over the face of the sky a space of
nearly 13°, so that at the same time, night after night, she
shifts her place to this amount, and therefore rises and
sets later. Now, if the Moon's orbit were exactly in the
plane of the ecliptic, we should not only have two eclipses
every month (as was remarked in Art. 233), but she would
appear always to follow the Sun's beaten track. We have
seen, however, that her orbit is inclined 5° to the plane
of the ecliptic, and therefore to the Sun's apparent path.
It follows, therefore, that when the Moon is approaching
her descending node, her path dips down (and her north
latitude decreases), and that when she is approaching
her ascending node her path dips up (and her southern
latitude decreases). Further, although the plane of her
path can never be more than 5° from the Sun's path, she
may be much more than 5° from that of the Sun's path,
at any one time, for she may be at the extreme south of
the ecliptic, while the Sun is at the extreme north, and
vice versa. The greatest difference between the meridian
altitudes of the Moon is twice 5°-}- 23^° = 57°; that is
to say, she may be 5° north of a part of the ecliptic,
which is 23^° north of the equator, or she may be 5°
south of a part of the ecliptic, which is 23^° south of
the equator.
371. But let us suppose the Moon to move actually in
the ecliptic— this will make what follows easier. It is
clear that the full Moon at midnight occupies exactly the
opposite point in the ecliptic to that occupied by the Sun
at noon-day. In winter, therefore, when the Sun is lowest,
the Moon is highest ; and so in winter we get more moon-
light than in summer, not only because the nights are
longer, but because the Moon, like the Sun in summer,
is apparently best situated for lighting up the northern
hemisphere.
172
ASTRONOMY.
372. Although, as we have seen, the Moon advances
about 13° in her orbit every 24 hours, the time between two
successive moonrises varies considerably, and for a reason
which should easily be understood. If the Moon moved
along the equator, — or, in other words, if her orbit were
in the plane of our equator, — the interval would always be
about the same, because the equator is always inclined the
same to our horizon ; but she moves nearly along the
ecliptic, which is inclined 23° to the equator; and because
Pig. 32. — Explanation of the Harvest Moon.
it is so inclined, she approaches the horizon at vastly
different angles at different times. In Art. 362 we saw
that half of the ecliptic is to the north and half to the
south of the equator, the former crossing the latter in the
signs Aries and Libra. Now when the Moon is furthest
from these two points twice a month, her path is parallel
with the equator, and the interval between two risings will
be nearly the same for two or three days together ; but
APPARENT MO VEMENTS. 1 73
mark what happens if she be near a node, i.e. in Aries
or Libra. In Aries the ecliptic crosses the equator to
the north; in Libra the crossing is to the south. In
Fig. 32 the line H O represents the horizon, looking east ;
EQ the equator, which in England is inclined about 38°
to the horizon. The dotted line EC represents the di-
rection of the ecliptic when the sign Libra is on the
horizon ; and the dotted line E'C' the direction of the
ecliptic when the sign Aries is on the horizon.
373. Now, as the Moon appears to rise because our
horizon is carried down towards it, it follows that when the
Moon occupies the three successive positions shown on
the line E'C' she will rise nearly at the same time on
successive evenings, because, as her path is but little in-
clined to the horizon, she therefore seems to travel nearly
along the horizon ; whereas, in the case of the line
EC, her path is more inclined to the horizon than the
equator itself. This, of course, happens every month, as
the Moon courses the whole length of the ecliptic in that
time ; but when the/"// Moon happens at this node, as it
does once a year, the difference comes out very strongly,
and this Full Moon is called the harvest moon, as it is
the one which falls always within a fortnight of Sept. 23,
the time of harvest.
374-. The planets, when they are visible, appear as
stars, and, like the stars, they rise and set by virtue of
the Earth's rotation. Their apparent motions among the
stars caused by the Earth's revolution round the Sun,
combined with their own actual movements, therefore
need only occupy our attention.
375. Let us glance at Plate V., and suppose that all
the planets there shown — the Earth among them — are
revolving round the Sun at different rates of speed, as is
actually the fact ; it will be at once clear that the distances
174 ASTRONOMY.
of the planets from each other and from the Earth are
perpetually varying ; the distances of all from the Sun,
however, remaining within the limits defined by the
degree of ellipticity of their orbits.
376. At some point of the Earth's path she will have
each planet by turns on the same side of the Sun as her-
self, and on the opposite side; it is evident therefore that
the extreme distances will vary in each case by the dia-
meter of the Earth's orbit, — that is, roughly, by 182,000,000
miles. But this is not all ; as the orbits are elliptical,
when the Earth and any one planet are near each other,
the distance will not always be the same ; for as these
approaches occur in different parts of the orbit, at one
time we may have both the Earth and planet at their
perihelion or aphelion points, or one may be in perihelion
and the other in aphelion. The same when the Earth
and any planet are on opposite sides of the Sun. This
will be exemplified presently.
377. The following table shows the average least and
greatest distances of each planet from the Earth, not
taking into consideration the variation due to the ellip-
ticity of the orbits : —
Least Distances. Greatest Distances.
Miles. Miles.
Mercury. . . 56,038,000 . . . 126,823,000
Venus . . . 25,299,000 . . . 157,562,000
Mars . . . 47,882,000 . . . 230,742,000
Jupiter . . . 384,263,000 . . . 567,123,000
Saturn . . . 780,704,000 . . . 963,565,000
Uranus . . 1,662,421^000 . . 1,845,281,000
Neptune . 2,654,841,000 . . 2,837,701,000
The first column, in fact, is the difference
between the distances of any one planet and
the Earth from the Sun, and the second column
is their sum. To this change of distance is to be
A P PARENT MO VEMENTS. 1 7 5
ascribed the change of brilliancy of the various planets,
due to their varying apparent sizes, as of course they
appear larger when they are near us than they do v/hen
they are on the other side of the Sun; and also their
phases, which, in the case of the planets whose orbits lie
between us and the Sun, are similar to those of the Moon,
and for a like reason. The difference of size will of
course depend upon the difference of distance, and the
difference of distance will be greatest for those planets
whose orbits lie nearest that of the Earth, as shown in the
table. Thus Venus when nearest the Earth appears six
times larger than when it is furthest away, because it is
really six times nearer to us ; Mars in like manner ap-
pears five times larger ; while in the case of Uranus and
Neptune, as the diameter of the Earth's orbit is small
compared with their distance from the Sun, their apparent
sizes are hardly affected.
In the case of the planets which lie between us and the
Sun, phases similar to those of the Moon are seen from
the Earth, because sometimes the planet is between us
and the Sun, similarly to what happens at New Moon ;
sometimes the Sun is between us and the planet, and con-
sequently we see the lit-up hemisphere. At other times,
as shown in Fig. 33, the Sun is to the right or left of the
planet as seen from the Earth; and we see a part of
both the lit-up and dark portions. Among the superior
planets, Mars is the only one which exhibits a marked
phase, which resembles that of the gibbous Moon.
378. To distinguish the planets which travel round
the Sun within the Earth's orbit, from those which lie
beyond us, the former, i.e. Mercury and Venus, are termed
inferior planets ; and the latter, i.e. Mars, Jupiter, Saturn,
Uranus arid Neptune, are termed superior planets.
When an inferior planet is in a line between the Earth
and Sun, it is said to be in inferior conjunction with
176 ASTRONOMY.
the Sun : when it is in the same line, but beyond the Sun,
it is said to be in superior conjunction. When a superior
planet is on the opposite side of the Sun, — that is, when
the Sun is between us and it, — we say it is in conjunction;
when in the same straight line, but with the Earth in the
middle, we say it is in opposition, because it is then in
the part of the heavens opposite to the Sun.
LESSON XXXI. — APPARENT MOTIONS OF THE PLANETS
(continued). ELONGATIONS AND STATIONARY POINTS.
SYNODIC PERIOD, AND PERIODIC TIME.
379. If an observer could watch the motions of the
planets from the Sun, he would see them all equally pursue
their beaten tracks, always in the same direction, with
different velocities, but with an almost even rate of speed
in the case of each. Our Earth, however, is not only a
moveable observatory, the motion of which complicates
the apparent movements of the planets in an extraordi-
nary degree, but from its position in the system all the
planets are not seen with equal ease. In the first place,
it is evident that only the superior planets are ever visible
at midnight, as they alone can ever occupy the region
opposite to the Sun's place at the time, which is the
region of the heavens brought round to us at midnight
by the Earth's rotation. Secondly, it is evident not
only that the inferior planets are always apparently near
the Sun, but that when nearest to us their dark sides are
turned towards us, as they are then between us and the Sun,
and the Sun is shining on the side turned away from us.
380. The greatest angular distance, in fact, of Mercury
and Venus from the Sun, either to the east (left) or west
A PPA RENT MO VEMENTS. 1 77
(right) of it, called the eastern and western elongations,
is 29° and 47° respectively. As a consequence, our only
chance of seeing these planets is either in the day-time
(generally with the aid of a good telescope), or just before
sunrise at a western elongation, or after sunset at an
eastern elongation. When Venus is visible in these
positions, she is called the morning star and evening
star respectively.
381. In Fig. 33 are shown a planet which we will first
take to represent the Earth in its orbit, and an inferior
planet at its conjunctions and elongations. In the first
place it is obvious that, as stated in Art. 377, such a
planet must exhibit phases exactly as the Moon does,
and for the same reason; and secondly, that the rate and
direction, as seen from the Earth, which for the sake of
simplicity we will suppose to remain at rest, will both
vary. At superior conjunction the planet will appear to
progress in the true or direct direction pointed out by
the outside arrow, but when it arrives at its eastern
elongation it will appear to be stationary, because it is
then for a short time travelling exactly towards the Earth.
From this point, instead of journeying from right to left,
as at superior conjunction, it will appear to us to travel
from left to right, or retrograde, until it reaches the
point of westerly elongation, when for a short time it
will travel exactly from the Earth, and again appear
stationary, after which it recovers its direct motion.
The only difference made by the Earth's own move-
ments in this case is, that as its motion is in the same
direction as that of the inferior planet, the times between
two successive conjunctions or elongations will be longer
than if the Earth were at rest.
382. As seen from the Earth, the superior planets
appear to reach stationary points in the same manner,
but for a different reason. At the moment a superior
N
T78 ASTRONOMY.
planet appears stationary, the Earth, as seen from
that planet, has reached its point of eastern or
western elongation. In fact, let P in Fig. 33 repre-
sent a superior planet at rest, and let the inferior planet
represented be the Enrth. Erom the western elongation
F*g- 33 — Diagram explaining the Retrogradations, Elongations, and
Stationary Points of Planets.
through superior conjunction, the motion of the planet
referred to the stars beyond it will be direct — i.e. from
*i to *2, as shown by the outside arrow ; when the Earth
is at its eastern elongation, as seen from the planet, the
planet as seen from the Earth will appear at rest, as we
are advancing for a short time straight to it. When this
point is passed, the apparent motion of the planet will be
reversed; it will appear to retrograde from *2 to *i,
as shown by the inside arrow.
383. As in the former case, the only difference when
we deal with the planet actually in motion, will be that the
times in which these changes take place will vary with
the actual motion of the planet ; for instance, it will
much less in the case of Neptune than in the case
Mars, as the former moves much more slowly
A F PARE NT MO VEMENTS. 1 79
38-4. In consequence of the Earth's motion, the period
in which a planet regains the same position with regard
to the Earth and Sun is different from the actual period
of the planet's revolution round the Sun. The time in
which a position, such as conjunction or opposition, is
regained, is called a synodic period. They are as follow
for the different planets : —
Mean Solar
Days.
Mercury. ....... 115*87
Venus ..... . . 583-92
Mars ..... ... 779'94
Jupiter ..... . . 398*87
Saturn ....... 378*09
Uranus ....... 369'66
Neptune . . . .' . , 367*49
Now these synodic periods are the periods actually ob-
served, and from which the times of revolution of the
planets round the Sun, or their periodic times, have been
found out. This is easily done, as follows : Let us repre-
sent the periodic times of any two planets by O and I ;
O representing the outside planet of the two, and I the
inside one ; and let us begin with the Earth and Mercury.
As the periodic time is the time in which a complete
circuit round the Sun, or 360°, .is accomplished ; in one
day, as seen from the Sun, the portion of the orbit passed
over would be equal to 360° divided by I and O ; or — —
and *— 9 the difference between these, or -j -- ~,
will be the number of degrees which the inside planet
gains daily on the outside one.
385. The actually observed interval from one conjunc-
tion of the two planets to the next, we will represent by
T ; but it is evident that in this time the inner one has
N 2
i8o ASTRONOMY.
gained exactly one complete revolution, or 360°, upon the
outer one ; in fact, the outer one will have advanced a
certain distance, and the inner one will have completed a
revolution, and in addition advanced the same distance
before the two planets are together again. Therefore,
360°
— will represent the daily rate of separation, which we
360° 360°
have seen is also shown by — |— — -Q— ;
360° 360° 360°
we may therefore say -^- = ~=— - ,, . . . (i)
In this case we want to know I, or the periodic time of
Mercury, and we know by observation, T, the synodic
period of Mercury and the Earth, which is given in the
previous table as 115*87 days, and O, the time of revolu-
tion of the Earth =» 365-256 days. We therefore trans-
pose the equation to get the unknown quantity on one
side, and the known ones on the other : we get
360° _ 3_6o° 360°
I T O
Dividing by 360°, we also get —
I . JL .1.
IT r O
Substituting the known values, we have
1 -L +JL
i 115*87 365-256.
Finding the value of this fraction, we get
i i
i" 877,
and therefore
I = 87-7 days.
APPARENT MO VEMENTS. \ 8 1
386. Next let us take the Earth and Jupiter. In this
case, as Jupiter is now the outside planet, we must trans-
pose equation (i) : —
360^ 360° _ 3_6o°
T I O
into
3_6o° _ 360^ _ 360°
O I T
as O, or the periodic time, is the unknown quantity, and
I and T are the two known ones. Proceeding as before,
we get
i i r
O == 365-256 ~~ ^98-87 ;
I I
r O " 433-2-9
or O = 4332*9 days.
The periodic time of Jupiter is therefore 4332*9 days.
387. We may also use equation (i) when, having the
periodic times of two planets given, we wish to determine
their synodic time. In this case T is the unknown
quantity, and I and O the known ones. Let us take the
Earth and Mars, whose periodic times are nearly 365-256
and 686*9 respectively. We have
i i i
T = T " O'
' T == 365^56 ~ 686'9»
which is equal to
T
or T = 779-9 days.
182 ASTRONOMY.
LESSON XXXII. — APPARENT MOVEMENTS OF THE
PLANETS (continued}. INCLINATIONS AND NODES
OF THE ORBITS. APPARENT PATHS AMONG THE
STARS. EFFECTS ON PHYSICAL OBSERVATIONS.
MARS. SATURN'S RINGS.
388. If the motions of the planets were confined to
the plane of the ecliptic, the motions, as seen from the
Earth, would exactly resemble those of the Sun ; but
as we have seen, the orbits are all inclined somewhat to
that plane. Here is a table of the present inclinations,
and positions of the ascending nodes (Art. 233 ) :—
Inclination of Longitude of
Orbit. Ascending Node.
o / " o '
• - 45 57
. . 74 51
• • 47 59
. . 98 25
. . in 56
. . 72 59
Neptune . . . i 46 59 ... 130 6
389. A moment's thought will convince us that the
apparent distance of a planet from the plane of the ecliptic
will be greater, as seen from the Earth, if the planet is
nearer the Earth than the Sun at the time of observation ;
and it also follows that as the distance of the planet from
the Earth must thus be taken into account, the distance
above or below the plane of the ecliptic will not appear to
vary so regularly when seen from the Earth as it would
do could we observe it from the Sun.
Mercury
Venus .
Mars .
... 7 o 5
• - • 3 23 29
i c i 6
Jupiter .
Saturn .
Uranus .
. . . - i 18 52
... 2 29 36
... o 46 28
A PPA RENT MO VEMENTS. 1 83
3&O. Moreover,
it should be clear
that when the pla-
net is at a node, it
will always appear
in the ecliptic.
391. Fig. 34 re-
presents the path
of Venus, as seen
from the Earth
from April to Octo-
ber 1868. A study
of it should make
what has already
been said about
the apparent mo-
tions of the planets
quite clear. From
April to June the
planet's north lati-
tude is increasing,
while the node and
stationary point —
which in this case
are coincident,
though they arc-
not always so — arc
reached about the
25th of June. Th-
southern latitude
rapidly increases
until, on the Qth
August, the other
stationary - point
is reached, after
184
ASTRONOMY.
35- — Saturn's apparent Path from
which the south latitude
decreases again.
392. In Fig. 35 is re-
presented the path of
Saturn from 1862 to 1865.
A comparison of this with
the preceding figure shows
how the distance of a
planet from the Earth
influences the shape of
its path. In this case, as
the planet's own motion
is, unlike that of Venus,
apparently slow, the
Earth's circular motion
is as it were reflected,
and between each oppo-
sition we have a loop, the
ends, of which are repre-
sented by the stationary
points.
Moreover, it will be seen
that the planet during the
time was north of the
ecliptic, or in that part of
its orbit situated- above
the plane of the Earth's
motion round the Sun,
and that the north lati-
tude was increasing. Still,
for all this, it was situated
south of the equator, and
1862 to 1865.
its south declination, or its distance south of that line,
was increasing. Hence, year by year, although it is
getting more above the ecliptic, it is getting more below
APPARENT MOVEMENTS.
185
the equator. Let this be compared with what was said
about the motion of the Moon in Art. 370, and it will
be evident that when on the meridian the planet's height
36.— The Orbits of Mars and the Earth.
above the horizon will decrease, until the planet itself
reaches that part of the ecliptic 23 J° south of the equator
1 86 ASTRONOMY.
—in fact, until its position is near that occupied by the
Sun in mid-winter.
393. The apparent path of a planet, then, is moulded,
as it were, by the motions of the Earth and the inclina-
tion of its own orbit. If we examine into the position of
the orbit of Mars, for instance, more closely than wj
have hitherto done, we shall see how the ellipticity of the
orbit and its inclination affect our observations of the
physical features. Fig. 36 shows the exact positions in
space of the orbits of the Earth and Mars, and the amount
and direction of the inclination of their axes, and the line
of Mars' nodes : both planets are represented in the
positions they occupy at the winter solstice of the northern
hemisphere. The lines joining the two orbits indicate
the positions occupied by both planets at successive oppo-
sitions of Mars, at which times, of course, Mars, the Earth,
and the Sun are in the same straight line (leaving the
inclination of Mars' orbit out of the question).
394-. It is seen at a glance that. at the oppositions of
1830 and 1860 the two planets were much nearer together
than in 1867, or than they will be in 1869.
The figure also enables us to understand that in the
case of an inferior planet, if we suppose the perihelion
of the Earth to coincide in direction, or, as astronomers
put it, to be in the same heliocentric longitude as the
aphelion of the planet, it will be obvious that the con-
junctions which happen in this part of the orbits of both
will bring the bodies nearer together than will the con-
junctions which happen elsewhere. Similarly, if we suppose
the aphelion of the Earth to coincide with the perihelion
of a superior planet, as in the case of Mars, it will be
obvious that the opposition which happens in that part;
of the orbit will be the most favourable for observation.
The Earth's orbit, however, is practically so nearly
circular that the variation depends more upon the ecccn-
A PPA RENT MO I'EMENTS.
187
tricity of the orbits of the other planets than upon our
own.
The figure also shows us that when Mars is observed
at the solstice indicated, we see the southern hemisphere
of the planet better than the northern one ; while at those
i88 ASTRONOMY.
oppositions which occur when the planet is at the opposite
solstice, the northern hemisphere is most visible. But we
see the northern hemisphere in the latter case better than
we do the southern one in the former, because in the
Fig. 38. — Appearance of Saturn when the plane of the ring system passes
through the Earth.
latter case the planet is above the ecliptic, and we there-
fore see under it better ; and in the former it is below the
ecliptic, and we see less of the southern hemisphere than
we should do were the planet situated in the ecliptic.
*'*& 39- — Saturn, as seen when the north surface of the rings is presented to
the Earth.
395. Fig. 37 shows the same effect of inclination in
the case of the rings of Saturn. The plane of the rings
is inclined to the axis, and, like the axis, always remains
parallel to itself. A study of the figure will show that
APPARENT MO VEMENTS. 1 89
twice in the planet's year the plane of the rings must
pass through the Sun ; and while the plane is sweeping
across the Earth's orbit, the Earth, in consequence of its
rapid motion, may pass two or three times through the
plane of the ring. Hence the ring about this time maybe
invisible from three causes : (i) Its plane may pass through
the Sun, and its extremely thin edge only will be lit up.
(2) The plane may pass through the Earth ; and (3) the
Sun may be lighting up one surface, and the other -may
be presented to the Earth. These changes occur about
every fifteen years, and in the mid-interval the surface of
the rings — sometimes the northern one, at others the
southern — is presented to the Earth in the greatest
angle.
In Plate X. Saturn was represented with the south
surface of the rings presented to the Earth. In Fig. 38
the appearance when the plane of the ring passes through
the Earth is given ; and in Fig. 39 we have the aspect of
the planet when the north surface of the ring is visible.
CHAPTER V.
THE MEASUREMENT OF TIME.
LESSON XXXIII. — ANCIENT METHODS OF MEASURE-
MENT. CLEPSYDRAE. SUN-DIALS. CLOCKS AND
WATCHES. MEAN SUN. EQUATION OF TIME.
396. HAVING dealt with the apparent motions of the
heavenly bodies, we now come to what those apparent
motions accomplish for us, namely the division and exact
Measurement of Time. For common purposes, time is
measured by the Sun, as it is that body which gives us the
primary division of time into day and night ; but for
astronomical purposes the stars are used, as the apparent
motion of the Sun is subject to variation.
397. The correct measurement of time is not only
one of the most important parts of practical Astronomy,
but it is one of the most direct benefits conferred on man-
kind by the science ; it enters, in fact, so much into every
affair of life, that we are apt to forget that there was a
period when that measurement was all but impossible.
398. Among the contrivances which were to the an-
cients what clocks and watches are to us, we may mention
clepsydrae and sun-dials. Of these, the former seem the
more ancient, and were used not only by the Greeks and
Romans, but by other nations, both Eastern and Western,
MEASUREMENT OF TIME. 191
the ancient Britons among them. In its simplest form
it resembled the hour-glass, water being used instead of
sand, and the flow of time being measured by the flow
of the water. After the time of Archimedes, clepsydras of
the most elaborate construction were common ; but while
they were in use, the days, both winter and summer, were
divided into twelve hours from sunrise to sunset, and
consequently the hours in winter were shorter than the
hours in summer ; the clepsydra, therefore, was almost
useless except for measuring intervals of time, unless dif-
ferent ones were employed at different seasons of the year.
399. The sun-dial also is of great antiquity; it is re-
ferred to as in use among the Jews 742 B.C. This was a
great improvement upon the clepsydrae ; but at night and
in cloudy weather it could not be used of course, and the
rising, culmination, and setting of the various constella-
tions were the only means available for roughly telling
the time during the night. Indeed, Euripides, who lived
480-407 B.C., makes the Chorus in one of his tragedies
ask the time in this form : —
"What is the star now passing?"
and the answer is —
" The Pleiades show themselves in the East ;
The Eagle soars in the summit of heaven."
It is also on record that as late as A.D. 1 108 the sacristan
of the Abbey of Cluny consulted the stars when he wished
to know if the time had arrived to summon the monks to
their midnight prayers ; and in other cases, a monk re-
mained awake, and to measure the lapse of time repeated
certain psalms, experience having taught him in the day,
by the aid of the sun-dial, how many psalms could be
said in an hour. When the proper number of psalms had
been said, the monks were awakened.*
* Arago.
192
ASTRONOMY.
4-OO. To understand the construction of a sun-dial, let
us imagine a transparent cylinder, having an opaque axis,
both axis and cylinder being placed parallel to the axis of
the earth. If the cylinder be exposed to the sun, the
shadow of the axis will be thrown on the side of the
cylinder away from the sun ; and as the sun appears to
travel round the earth's axis in 24 hours, it will equally
Fig. 40. — Sun-dial. (AB, axis of cylinder; MNt PQ, two Sun-dials, con-
structed at different angles to the plane of the horizon, showing how the
imaginary cylinder determines the hour-lines. )
appear to travel round the axis of the cylinder in 24
hours, and it will cast the shadow of the cylinder's axis
on the side of the cylinder as long as it remains above
the horizon. All we have to do, therefore, is to trace on the
side of the cylinder 24 lines 15° apart (15 X 24 = 360),
taking care to have one line on the north side. When
MEASUREMENT OF TIME. 193
the sun is south at noon, the shadow of the axis will be
thrown on this line, which we may mark XII.; when the
sun has advanced one hour to the west, the shadow will
be thrown on to the next line to the east, which we may
mark I., and so on.
4-O1. The distance of the sun above the equator will
evidently make no difference in the lateral direction of the
shadow.
4-O2. In practice, however, we do not want such a
cylinder ; all we want is a projection called a style,
parallel to the earth's axis, like the axis of the cylinder,
and a dial. The dial may be upright or horizontal, or
inclined in any way so as to receive the shadow of the
style, but the lines on it indicating the hours will always
be determined by imagining such a cylinder, slicing it
down parallel to the plane of the dial, and then joining
the hour-lines on its surface with the style where it meets
the dial. We shall return to the sun-dial after we have
said something about clocks and watches.
4-O3. The principle of both clocks and watches is
that a number of wheels, locked together by cogs, are
forced to turn round, and are prevented doing so too
quickly. The force which gives the motion may be either
a weight or a spring : the force which arrests the too
rapid motion may either proceed from a pendulum, which
at every swing locks the wheels, or from some equivalent
arrangement.
4O4. The invention of clocks is variously ascribed to the
sixth and ninth centuries. The first clock in England was
made about 1288, and was erected in Old Palace Yard.
Tycho Brahe used a clock, the motion of which was
retarded or regulated by means of an alternating balance
formed by suspending two weights on a horizontal bar,
the movement being made faster or slower by altering the
distances of the weights from the middle of the bar. But
o
194 ASTRONOMY.
the Clock, as an accurate measurer of time, dates from the
time of Galileo (1639) and Huyghens (1656).
4-O5. In both clocks and watches we mark the flow
of time by seconds, such that sixty of them make a minute,
sixty of which make an hour, twenty-four of which make
a day. Those people who are not astronomers are quite
satisfied with this, and a day is a word with a certain mean-
ing. The astronomer, however, is compelled to qualify it —
to put some other word before it — or it means very little to
him, because, as we have seen (Art. 358), the term day may
mean either the return of a particular meridian to the same
star again or to the sun again. The term, as it is com-
monly used, means neither the one nor the other, because
long ago, when it was found that in consequence of the
motion of the earth not being uniform in its orbit round
the sun (Art. 359), the days, as measured by the sun, were
not equal in length, astronomers suggested, with a view of
establishing a convenient and uniform measure of time
for civil purposes, that a day should- be the average of all
the days in the year. So that our common day is not
measured by the true sun, as a sun-dial measures it, but
by what is called the mean (or average) sun.
4O6. For a long time after clocks and watches were
made with considerable accuracy, it was attempted to
make them keep time with the sun-dial, and for this
purpose they were regulated once a day, or once a week,
ignorant people taxing the maker with having supplied
an imperfect instrument, as it would not keep time with
the sun.
4-O7- Let us inquire into the motion of the imaginary
mean sun, by means of which the irregularities of the sun's
apparent daily motion, and the unequal hours we get as a
consequence from sun-dials, are obviated.
4O8. In the first place, the real sun's motion is in the
ecliptic, and is variable. Secondly, the sun crosses the
MEASUREMENT OF TIME.
'95
equator twice a year at the equinoxes, at an angle of
23 £°, and midway between the equinoxes— that is, at the
solstices — its path is almost parallel with the equator.
Therefore, the sun's ecliptic motion, referred to the
equator is variable, for two causes : —
I. The real motion is variable.
II. The motion is at different angles to the equator, and
therefore referred to that line is least when the angle is
greatest.
4O9. Let us first deal with the first cause — the in-
equality of the real sun's motion. When the earth is
nearest the sun, about Jan. i, the sun appears to travel
through i° i' 10" of the ecliptic in 24 hours ; at aphelion,
about July I, the daily arc is reduced to 57' 12." The
first thing to be done therefore is to give a constant
motion to the mean or imaginary sun. As the real sun
passes through 360° in 365 d. 5h. 48m. 47*8 s., we have
One year : one day : : 360° : daily motion;
and this rule of three sum tells us that the mean daily
motion = 59' 8"'33 ; and this therefore is the rate at
which the mean sun rs supposed to travel.
4-1O. If the true sun moved in the equator instead of in
the ecliptic, a table showing how far the mean and true
sun were apart for every day in the year would at once
enable us to determine mean time.
All. But the true sun moves along the ecliptic, while
the mean sun must be supposed to move along the equator ;
so that it may be carried evenly round by the earth's
rotation. This brings out the second cause of the in-
equality of the solar days. At some times of the year (at
the solstices) the true sun moves almost parallel to the
O 2
196 ASTRONOMY.
equator, at other times (at the equinoxes) it cuts the
equator at an angle of 23^° ; and when its motion is re-
ferred to the equator, time is lost. This will be rendered
evident if on a celestial globe we place wafers, equally
distant from the first point of Aries, both on the equator
and the ecliptic, and bring them to the brass meridian.
412. We have, then, the mean sun, not sup-
posed to move along the ecliptic at all, but
along the equator, at an uniform rate of o° 59' 8"'3
a dav (= f§I days)' and started> so to speak, from the
first point of Aries, where the ecliptic and equator cut
each other, and at such a rate that, supposing the true sun
to move along the ecliptic at an uniform rate, the positions
of the true sun referred to the equator will correspond
with the mean sun at the two solstices and the two
equinoxes.
4-13. If the motion of the true sun were uniform, a
correct clock would correspond with a correct
sun-dial at these periods; between these periods they
would indicate different times, as the true sun would lose
time in climbing the heavens at its start from the point
of intersection in Aries, and so on.
414-. But we know the motion of the true sun is not
uniform ; it moves fastest when the earth is
in perihelion, slowest when the earth is in
aphelion ; and if we also take this irregular motion
into account, we find that the motion of the real sun in
the ecliptic is nearly equal to the motion of the mean
sun in the equator four times a year, namely,—
April 1 5th. I Aug. 3ist.
June I5th. Dec. 24th.
4-15. At these dates we shall find the sun-dial and
clock corresponding, but at the following dates we shall
find differences as follows : —
MEASUREMENT OF TIME. 197
Minutes.
Feb. nth -f 14^
May I4th 4
July 25th + 6
Nov. ist — i6£
which are the differences in time between the true and
mean sun. Hence it is that in the almanacs we find what
is termed the equation of time given, which is the time we
must add to or subtract from the time shown by a sun-
dial, to make the dial correspond with a good clock. For
instance, at the period of the year at which the mean
sun is before the true sun, the clock will be before the
dial, and we must add the equation of time to the time
shown by the true sun.
4-16. When the earth is in perihelion, or — what comes
to the same thing— when the sun is in perigee, the real
sun moves fastest, and therefore will gain on the mean sun,
and the dial will be before the clock. When
the sun is in apogee, the mean sun will move fastest, and
the clock will be before the dial. The equation
of time will therefore be additive or subtractive, or, as it
is expressed, -f- or — with regard to the time shown by
the true sun, or to apparent time.
417. So, to refer back to Art. 41 5, in November we must
deduct i6|m. from the apparent time, and in February we
must add I4^m. to apparent time, to get clock time. In
November, therefore, the true sun sets i6m. earlier than
it would do if it occupied the position of the mean sun, by
which our clocks are regulated. In February it sets 1 5m.
later, and this is why the evenings begin to lengthen after
Christmas more rapidly than they would otherwise do.
418. We cannot obtain mean time at once from obser-
vation ; but, from an observation of the true sun with the
aid of the equation of time, which is the angular distance
in time between the mean and the true sun, we may
198 ASTRONOMY
readily deduce it. Suppose the true sun to be observed
on the meridian of Greenwich, Jan. i, 1868 : it would then
be apparent noon at that meridian ; the equation of time
at this instant is 3m. 36*63 s. as given in the almanacs,
and is to be added to apparent time; hence the corre-
sponding mean time is Jan. i, oh. 3m. 36-63 s.; that is
to say, the mean sun had passed the meridian previously
to the true sun, and at the instant of observation the
mean time clock ought to indicate this time.
LESSON XXXIV.— DIFFERENCE OF TIME. How DE-
TERMINED ON THE TERRESTRIAL GLOBE. GREEN-
WICH MEAN TIME. LENGTH OF THE VARIOUS DAYS.
SIDEREAL TIME. CONVERSION OF TIME.
4-19. Having said so much of solar days, both apparent
and mean, we must next consider the start-points of
these reckonings. We have — I. the apparent solar day,
reckoned from the instant the true sun crosses the meri-
dian through 24 hours, till it crosses it again ; II. the
mean solar day, reckoned by the mean sun in the same
manner. Both these days are used by astronomers.
III. The civil day commences from the preceding mid-
night, is reckoned through 12 mean hours only to noon,
and then recommences, and is reckoned through another
12 hours to the next midnight. The civil reckoning is
therefore always 12 hours in advance of the astronomical
reckoning ; hence the well known rule for determining the
latter from the former, viz. : — For P.M. civil times, make no
change ; but for A.M. ones, diminish the day of the month
by i and add 12 to the hours. Thus : Jan. 2, 7h. 49m.
P.M. civil time, is Jan. 2, 7h. 49111. astronomical time;
MEASUREMENT OF TIME. 199
but January 2, 7h. 49111. A.M. civil time is January i,
I9h. 4901. astronomical time.
420. Now the position of the sun, as referred to the
centre of the earth, is independent of meridians, and is the
same for all places at the same absolute instant ; but the
time at which it transits the meridian of Greenwich, and
any other meridian, will be different. In a mean solar day,
or 24 mean solar hours, the earth, by its rotation from
west to east, has caused every meridian in succession from
east to west to pass the mean sun ; and since the motion
is uniform, all the meridians distant from each other 1 5°
will have passed the mean sun, at intervals of one mean
hour ; the meridian to the eastward passing first, or being,
as compared with the sun, always one mean hour in
advance of the westerly meridian. When it is 6 hours
after mean noon at a place 15° west of Greenwich, it is
therefore 7 hours after mean noon at Greenwich. When
it is noon at Greenwich, it is past noon at Paris, because
the sun has apparently passed over the meridian of Paris
before it reached the meridian of Greenwich Similarly,
it is not yet noon at Bristol, for the sun has not yet reached
the meridian of Bristol.
421. In civilized countries, at the present moment, not
only is the use of mean time universal, but the mean
time of the principal city or observatory is
alone used. In England, far instance, Greenwich
mean time (written G.M.T. for short) is used : in France,
Paris mean time; in Switzerland, Berne mean time, and
so on. This has become necessary owing, among other
things, to the introduction of railways, so that with us
Greenwich mean time is often called railway time. For-
merly, before local time was quite given up, the churches
in the West of England had two minute-hands, one show-
ing local time, the othei Greenwich time.
4-22. On the Continent, railway-stations near the
200 ASTRONOMY.
frontier of two states have their time regulated by their
principal Observatories. At Geneva, for instance, we see
two clocks, one showing Paris time, and the other Berne
time ; and it is very necessary to know whether the time
at which any particular train we may wish to travel in
starts, is regulated by Paris or Berne time, as there is a
considerable difference between them.
4-23. Expressed in mean time, the length of the day is
as follows : —
Apparent solar day (Art. 419) . . . variable.
h. m. s.
Mean solar day (Art. 419) .... 24 o o
Sidereal day (Art. 358) 23 56 4-09
Mean lunar day 24 54 o
4-24. It will be explained further on (Chap. VII.) that
sidereal time is reckoned from the first point of Aries, and
that when the mean sun occupies the first point of Aries •,
which it does at the vernal equinox, the indications of the
mean-time clock and the sidereal clock will be the same ;
but this happens at no other time, as the sidereal day is
but 23 h. 56 m. 4 s. (mean time) long, so that the sidereal
clock loses about four minutes a day, or one day a year
(of course the coincidence is established again at the next
vernal equinox), as compared with the mean time one.
425. A sidereal clock represents the rotation of the
earth on its axis, as referred to the stars, its hour-hand
performing a complete revolution through the 24 sidereal
hours between the departure of any meridian from a
star and its next return to it ; at the moment that the
vernal equinox, or a star whose right ascension is
oh. om. os is on the meridian of Greenwich, the sidereal
clock ought to show oh. om. os., and at the succeeding
return of the star, or the equinox, to the same meridian,
the clock ought to indicate the same time.
.
MEASUREMENT OF TIME. 201
426. Sidereal time at mean noon, therefore, is the
angular distance of the first point of Aries, or the true
vernal equinox, from the meridian, at the instant of mean
noon : it is therefore the right ascension of the mean
sun, or the time which ought to be shown by a sidereal
clock at Greenwich, when the mean-time clock indicates
oh. om. os.
427. The sidereal time at mean noon for each day is
given in the " Nautical Almanac.'' Its importance will
be easily seen from the following rules : —
RULE I. — To convert mean solar into sidereal time:—
To the sidereal time at the preceding mean noon add the
sidereal interval corresponding to the given mean time ;
the sum will be the sidereal time required.
RULE II. — To convert sidereal into mean solar time :—
To the time at the preceding sidereal noon, add the mean
interval corresponding to the given sidereal time; the
sum will be the mean solar time required.
428. Tables of intervals are given in the Appendix,
showing the value of seconds, minutes, &c of sidereal
time in mean time, and vice versd.
429. Suppose, for instance, we wish, under Rule I. to
convert 2h. 22m. 25*625. mean time at Greenwich, Jan. 7,
1868, into sidereal time, we proceed as follows : —
Sidereal time at &£ preceding mean noon )
i.e. Jan. 7, from " Nautical Almanac " }
h. m. s.
19 5 22-34
h. ID. s.
T- ( 2 O O
For mean \
time inter- <
vals / 5
We get in the (
table, equiva- 1
lent sidereal 1
2 0 I97I3
22 3-614
25-069
( 0-62
intervals. (
0*622
The sum is the sidereal time required . . 21 28 ii'36
202 ASTRONOMY.
43O. Suppose we wish, under Rule II. to convert
2ih. 28m. 11*363. sidereal time at Greenwich, Jan. 7,
1868, into mean time, we proceed as follows : —
Mean time at the preceding sidereal
For side-
real in-
tervals.
The sum is the meantime required, Jan. 7 . 2 22 25*62
h. m. s.
21 0 0 ]
28 o (
o-36J
1 The table
gives the
equivalent
1 mean intervals
;
!20 56 33'579
27 55-4I3
IO*970
0-359
4-31. If the place of observation be not on the meridian
of Greenwich, the sidereal time must be corrected by the
addition of 9*85655 for each hour (and proportional parts
for the minutes and seconds) of longitude, if the place be
to the west of Greenwich ; but by its subtraction, if to the
east. Thus in 9h. lorn. 6s. west longitude, the sidereal
time at mean noon, Jan. 7, 1868, instead of being, as in
the foregoing examples, I9h.5m. 22*345. must be corrected
by adding iin. 30*375., thus giving 19!!. 6m. 53*1 is. for
the time to be used, instead of that set down in the
column.
LESSON XXXV.— THE WEEK. THE MONTH. THE
YEAR. THE CALENDAR. OLD STYLE. NEW STYLE.
432. Although the week, unlike the day, month, and
year, is not connected with the movements of any
heavenly body, the names of the seven days of which it
is composed were derived by the Egyptians from the
MEASUREMENT OF TIME. 203
seven celestial bodies then known. The order of succession
established by them was continued by the Romans, their
names being as follow : —
Dies Saturni . . Saturn's day . . Saturday.
Dies Soils . . . Sun's day . . . Sunday.
Dies Lunce . . . Moon's day . . Monday.
Dies Martis . . Mars' day . . . Tuesday.
Dies Mercurii. . Mercury's day . . Wednesday.
Dies Jovis . . . Jupiter's day . . Thursday.
Dies Veneris . . Venus's day . . Friday.
4-33. We see at once the origin of our English names
for the first three days ; the remaining four are named
from Tiu, Woden, Thor, and Friga, Northern deities
equivalent to Mars, Mercury, Jupiter, and Venus in the
classic mythology.
4-34.. We next come to the month. This is a period of
time entirely regulated by the moon's motion round the
earth (see Lesson XVI.).
The lunar month is the same as the lunation or synodic
month, and in the time which elapses between the con-
secutive new or full moons, or in which the moon returns
to the same position relatively to the earth and sun.
The tropical month is the revolution of the moon with
respect to the moveable equinox.
The sidereal month is the interval between two succes-
sive conjunctions of the moon with the same fixed star.
The anomalistic month is the time in which the moon
returns to the same point (for example, the perigee or
apogee) of her moveable elliptic orbit
The nodical month is the time in which the moon
accomplishes a revolution with respect to her nodes, the
line of which is also moveable.
The calendar month is the month recognised in the
almanacs, and consists of different numbers of days, such
as January, February, £c.
204 ASTRONOMY.
435. The lengths of these various months are as
follow : —
Mean Time,
d. h. m. s.
Lunar, or Synodic month . . 29 12 44 2-84
Tropical month 27 7 43 471
Sidereal „ 27 7 43 11-54
Anomalistic month . . . . 27 13 1 8 37*40
Nodical „ , .... 27 5 5 35-60
4-36. We next come to the year. This is a term
applied to the duration of the earth's movement round
the sun, as the term " day " is applied to the duration of
the earth's movement round its own axis ; and there are
various sorts of years, as there are various sorts of days.
Thus, we may take the time that elapses between two
successive conjunctions of the sun, as seen from the earth,
with a fixed star. This is called the sidereal year.
4-37. Again, we may take the period that elapses be-
tween two successive passages through the vernal equinox.
This is called the solar, or tropical year, and its length
is shorter than that of the sidereal one, because, owing to
the precession of the equinoxes, the vernal equinox in its
recession meets the sun, which therefore passes through
it sooner than it would otherwise do.
438. Again, we may take the time that elapses between
two successive passages of the earth through the peri-
helion or aphelion ; point and as these have a motion
forward in the heavens, it follows that this year, called the
anomalistic one, will be longer than the sidereal one.
439. The exact lengths of these years are as follow : —
Mean Time,
d. h. m. s.
Mean sidereal year .... 365 6996
Mean^ solar or tropical year . 365 5 48 46*054440
Mean anomalistic year . . . 365 6 13 49*3
MEASUREMENT OF TIME. 205
4-4-O. It is seen from this table that the solar year does
not contain an exact number of solar days, but that in
each year there is nearly a quarter of a day over. It is said
that the inhabitants of ancient Thebes were the first to
discover this. The calendar had got in such a state of
confusion in the time of Julius Caesar, that he called in
the aid of the Egyptian astronomer Sosigenes to reform
Fit. He recommended that one day, every four years, should
be added by reckoning the sixth day before the kalends
of March twice ; hence the term bissextile.
4-4.1. With us, in every fourth year one additional day
is given to February. Now this arrangement was a very
admirable one, but it is clear that the year was over-
corrected. Too much was added, and the matter was again
looked into in the sixteenth century, by which time the over-
correction had amounted to more than ten days, the vernal
equinox falling on March u, instead of March 21. Pope
Gregory, therefore, undertook to continue the good work
begun by Julius Caesar, and made the following rule for
the future : — Every year divisible by 4 to be a bissextile,
or leap-year, containing 366 days ; every year not so
divisible to consist of only 365 days ; every secular year
(1800, 1900, &c.) divisible by 400 to be a bissextile, or
leap-year, containing 366 days ; every secular year not so
divisible to consist of 365 days.
44-2. The period by which the addition of one day in
four years exceeds the proper correction amounts to
nearly three days in 400 years ; by the new arrangement
there are only 97 intercalations in 400 years, instead
of ico. This brings matters within 22*385. in that period,
which amounts to i day in 3866 years.
44-3. The Julian calendar was introduced in the year
44 B.C.; the reformed Gregorian one in 1582. It was not
introduced into this country till 1752, in consequence of
religious prejudices. With us the correction was made
206 ASTRONOMY.
by calling the day after Sept. 3, 1752, Sept. 14. This was
called the new style (N.S.), as opposed to the old style
(O.S.). In Russia the old style is still retained, although
it is customary to give both dates, thus : 1868 ^~^
44-4. It is impossible to overrate the importance of these
various improvements devised for a better knowledge of
the length of the tropical or solar year : if the calendar
were not exactly adjusted to it, the seasons would not
commence on the same day of the same month as they
do now, but would in course of time make the com-
plete circuit of all the days in the year ; January, or any
other month, might fall either in spring, summer, autumn,
or winter.
44-5. At present, owing to a change of form in the
Earth's orbit (Chap. IX.), the tropical year diminishes in
length at the rate of y^ths of a second in a century, and it
is shorter now than it was in the time of Hipparchus by
about 12 seconds.*
446. If the tropical and the anomalistic year were of
equal lengths, it would follow that, as the seasons are
regulated by the former, they would always occur in the
same part of the Earth's orbit. As it is, however, the line
joining the aphelion and perihelion points, termed the
line of apsides, slowly changes its direction at such a
rate that in a period of 21,000 years it makes a complete
revolution. We have seen before (Art. 167) that at
present we are nearest to the sun about Christmas time.
In A.D. 6485 the perihelion point will correspond to the
vernal equinox.
447. As the length of the seasons, compared with
each other, depends upon the elliptical shape of the Earth's
orbit, it follows that variations in the relative lengths will
arise, from the variation in the position of its largest
diameter.
* Hind.
CHAPTER VI.
LIGHT.— THE TELESCOPE AND SPECTROSCOPE.
LESSON XXXVL— WHAT LIGHT is ; ITS VELOCITY;
HOW DETERMINED. ABERRATION OF LIGHT. REFLEC-
TION AND REFRACTION.. INDEX OF REFRACTION
DISPERSION. LENSES.
Modern science teaches us that light consists of
undulations or waves of a medium called ether, which
pervades all space. These undulations — these waves of
light — are to the eye what sound-waves are to the ear,
and they are set in motion by bodies at a high tempera-
ture— the Sun, for instance — much in the same manner as
the air is thrown into motion by our voice, or the surface
of water by throwing in a stone ; but though a wave-
motion results from all these causes, the way in which
the wave travels varies in each case.
449. As we have seen, light, although to us it seems
instantaneous, requires time to travel from an illuminat/ttg*
to an illuminate/ body, although it travels very quickly.
What has already been said about the planet Jupiter and
his moons will enable us readily to understand how the
velocity of light was determined by Roemer. He found
that the eclipses of the moons (which he had calculated
208 ASTRONOMY.
beforehand) happened 1 6m. 365. later when Jupiter was in
conjunction with the Sun than when he was in opposition.
Now we know (Art. 377) that Jupiter is further from us
in the former case than in the latter, by exactly the dia-
meter of the Earth's orbit. He soon convinced himself that
the difference of time was due to the light having so much
further to travel. Now the additional distance, i.e. the
diameter of the Earth's orbit, being 182,000,000 miles, it
follows by a rule-of-three sum that light travels about
186,000 miles a second. This fact has been abundantly
proved since Roemer's time, and what astronomers call
the aberration of light is one of the proofs.
B C
Fig. 41. — Showing how a tube in movement from C to B must be inclined
so that the drop a may fall to b without wetting the sides.
45O. We may get an idea of the aberration of light by
observing the way in which, when caught in a shower,
we hold the umbrella inclined in the direction in which
we are hastening, instead of over head, as we should do
were we standing still. Let us make this a little clearei.
Suppose I wish to let a drop of water fall through a tube
LIGHT. 209
without wetting the sides : if the tube is at rest there is no
difficulty, it has only to be held upright in the direction A B ;
but if we must move the tube the matter is not so easy
The diagram shows that the tube must be inclined, or
else the drop in the centre of the tube at a will no longei
be in the centre of the tube at b\ and the faster, the
tube is moved the more must it be inclined. Now we
may liken the drop to rays of light, and the tube to the
telescope, and we find that to see a star we must incline
our telescopes in this way. By virtue of this, each star
really seems to describe a small circle in the heavens,
representing on a small scale the Earth's orbit ; the
extent of this apparent circular motion of the star depend-
ing upon the relative velocity of light, and of the Earth
in its orbit, as in Fig. 41 the slope of the tube depends
Fig. 42. —Showing how a ray coming from a star in the direction A B changes
its direction, in consequence of the refraction of the atmosphere.
upon the relative rapidity of the motion of the tube and
of the drop ; and we learn from the actual dimensions of
the circle that light travels about 10,000 times faster
than the Earth does — that is, about 186,000 miles a
second. This velocity has been experimentally proved
by M. Foucault, by means of a turning mirror.
451. Now a ray of light is reflected by bodies which lie
in its path, and is refracted, or bent out of its course, when
P
210 ASTRONOMY.
it passes obliquely from a transparent medium of a certain
density, such for instance as air, into another of a different
density, such as water.
4-52. By an effect of refraction the stars appear to
be higher above the horizon than they really are. In
Fig. 42, A B represents a pencil of light coming from a
star. In its passage through our atmosphere, as each
layer gets denser as the surface of the Earth is approached,
the ray is gradually refracted until it reaches the surface
at C, so that from C the star seems to lie in the direc-
tion CB.
453. The refraction of light can be best studied by
means of a piece of glass with three rectangular faces,
Fig. 43.— A Prism, showing its action on a beam of light.
called a prism. If we take such a prism into a dark room,
and admit a beam of sunlight through a hole in the shutter,
and let it fall obliquely on one of the surfaces of the
prism, we shall see at once that the direction of the ray
is entirely changed. In other words, the angle at which
the light falls on the first surface of the prism is different
from the angle at which it leaves it. The difference
between the angles, however, is known to depend upon a
law which is expressed as follows : The sines of the
angles of incidence and refraction have a con-
stant proportion or ratio to one another. This
LIGHT. 2ti
ratio, called the index of refraction, varies in different
substances. For instance, it is — •
2 '9 for chromate of lead.
2*0 for flint glass.
1*5 for crown glass,
i -3 for water.
•454-. If we receive a beam after its passage through
the prism on a piece of smooth white paper, we shall see
that this is not all. Not only has the ray been bent
out of its original course bodily, so to speak, but instead
of a spot of white light the size of the hole which admitted
the beam, we have a lengthened figure of various colours,
called a spectrum.
455. This spectrum will be of the same breadth as the
spot which would have been formed by the admitted light,
had it not been intercepted by the prism. The lengthened
figure shows us, therefore, that the beam of light in its
passage through the prism must have been opened out,
the various rays of which it is composed having undergone
different degrees of deviation, which are exhibited to us by
various colours — from a fiery brownish red when the re-
fraction is least, to a faint reddish violet at the point of
greatest divergence. This is called dispersion.
4-56. If we pass the light through prisms of different
materials, we shall find that although the colours always
maintain the same order, they will vary in breadth or in
degree. Thus, if we employ a hollow prism, filled with
oil of cassia, we shall obtain a spectrum two or three
times longer than if we use one made of common glass.
This fact is expressed by saying that different media
have different dispersive powers— that is, disperse
or open out the light to a greater or less extent.
4-57. Every species of light preserves its own relative
place in the general scale of the spectrum, whatever be
p 2
212 ASTRONOMY.
the media between which the light passes, but only in
order, not in degree ; that is, not only do the different
media vary as to their general dispersive effect on the
different kinds of light, but they affect them in different
proportions. .If, for instance, the green, in one case,
holds a certain definite position between the red and the
violet, in another case, using a different medium, this
position will be altered.
This is what is termed by opticians the irrationality of
the dispersions of the different media— or shortly, the
irrationality of the spectrum.
4-58. What has been stated will enable us to understand
the action of a common magnifying-glass or lens. Thus
as a prism acts upon a ray of light, as shown in the
above Fig. 43, two prisms arranged as in Fig. 44 would
Fig. 44. —Action of two Prisms placed base to base.
converge two beams coming from points at a and b to
one point at c. A lens, we know, is a round piece of glass,
generally thickest in the middle, and we may look upon
it as composed of an infinite number of prisms. Fig. 45
shows a section of such a lens, which section, of course,
LIGHT. 213
may be taken in any direction through its centre, and
a little thought will show that the light which falls on
its whole surface will be bent to c, which point is called
the focus. If we hold a common burning-glass up to the
sun, and let the light fall on a piece of paper, we shall find
Fig. 45. — Action of a Convex Lens upon a beam of parallel rays.
that when held at a certain distance from the lens a hole
will be burned through it ; this distance marks the focal
distance of the lens. If we place an arrow, a b, in front of
the lens mn, we shall have an image of an arrow behind at
Fig. 46. — Showing how a Convex Lens, m «, with an arrow, a b, in front of it,
throws an inverted image, a' b' , behind it.
a' y, every point of the arrow sending a ray to every point
in the surface of the lens ; each point of the arrow, in
fact, is the apex of a cone of rays resting on the lens, and
a similar cone of rays, after refraction, paints every point
of the image. At a, for instance, we have the apex of a
214 ASTRONOMY.
cons of rays, man, which rays are refracted ; and' we
have another cone of rays, ma' n, painting the point a' in
the image. So with b, and so with every other point.
We see that the action of a lens, like the one in the
figure, thickest in the middle, called a convex lens, is to
invert the image. The line xy is called the axis of
the lens.
4-59. Such, then, is a lens, and such a lens we have in
our eye ; and behind it, where the image is cast, as in the
diagram, we have a membrane which receives the image
as the photographer's ground glass or prepared paper
does ; and when the image falls on this membrane, which
is called the retina, the optic nerves telegraph as it were
an account of the impression to the brain, and we see.
LESSON XXXVII. — ACHROMATIC LENSES. THE TE-
LESCOPE. ILLUMINATING POWER. MAGNIFYING
POWER.
4-6O. Now in order that we see, it is essential that the rays
should enter the eye parallel or nearly so, and the nearer
anything is to us the larger it looks ; but if we attempt to
see anything quite close to the eye, we fail, because the
rays are no longer parallel — they are convergent. Here
the common magnifying-glass comes into use ; we place
the glass close to the eye, and place the object to be
magnified in its focus, — that is, at c in Fig. 45 : the rays
which diverge from the object are rendered parallel by
the lens, and we are enabled to see the object, which
appears large because it is so close to us.
4-61. Similarly if we place a shilling twenty feet off, and
employ a convex lens, the focal length of which is five
LIGHT. 215
feet, half way between our eye and the shilling, we shall
have formed in front of the eye an image of the shilling,
which being within six inches of the eye, while the real
shilling is twenty feet off, will appear forty times larger,
although in this case the image is of exactly the same
size as the shilling. So much for the action of a single
convex lens.
4-62. Now, if instead of arranging the prisms as shown
in Fig. 44, with their bases together, we place them point
to point, it is evident that the rays falling upon them will
no longer converge, or come together to a point. They
will in fact separate, or diverge. We may therefore sup-
pose a lens formed of an infinite number of prisms, joined
together in this way ; such a lens is called a concave
Fig. 47. — Showing the action of a Bi-Concave Lens on a beam of
parallel rays.
and the shape o" any section of such a lens and its action
are shown in Fig. 47.
463. In some lenses one surface is flat, the other being
either concave or convex ; so besides the bi-convex and
bi-concave, already described, we have plano-convex and
plano-concave lenses.
464. Now we have already seen (Art. 458) that a lens is
but a combination of prisms ; we may therefore expect that
the image thrown by a lens will be coloured. This is the
210 ASTRONOMY.
case ; and unless we could get rid of it, it would be impos-
sible to make a large telescope worth using. It has been
found possible however to get rid of it, by using two
lenses of different shapes, and made of different kinds of
glass, and combining them ^together, so making a com-
bination called an achromatic, or colourless, lens.
4-65. This is rendered possible by the varying disper-
sive powers (Art. 455) of different bodies. If we take two
exactly similar prisms made of the same material, and
place one on its side and the other behind it on one of
its angles, the beam of light will be unaffected : one prism
will exactly undo the work done by the other, and the ray
will neither be refracted nor dispersed ; but if we take
away the second prism and replace it by one made of a
substance having a higher dispersive power, we shall of
course be able to undo the dispersive work done by the
first prism with a smaller thickness of the second.
But this smaller thickness will not undo all the refrac-
tive work of the first prism
Therefore the beam will leave the second prism colour-
less, but refracted ; and this is exactly what is wanted ;
the chromatic aberration is corrected, but the com-
pound prism can still refract, or bend the light out of its
course.
466. An achromatic lens is made in the same way as
an achromatic prism. The dispersive powers of flint and
crown glass are as '052 to '033. The front or convex lens
is made of crown glass. The chromatic aberration of
this is corrected by another bi-concave lens placed behind
it of flint glass. The second lens is not so concave as the
first is convex, so the action of the first lens is predomi-
nant as far as refraction goes ; but as the second lens acts
more energetically as regards dispersion, although it can-
not make the ray parallel to its original direction, it can
make it colourless, or nearly so. If such an achromatic
LIGHT.
217
lens be truly made, and its curves properly regulated,
said/to have its spherical aberration corrected as
as/its chromatic one, and the
rnage of a star will form a nearly
'colourless point at its focus.
467. A little examination into
the construction of the tele-
scope will show us that the prin-
ciple of its construction is iden-
tical with the construction of the
eye, but the process carried on
by the eye is extended : that is
to say, in the eye nearly parallel
rays fall on a lens, and this lens
throws an image; in the tele-
scope nearly parallel rays fall
on a lens, this lens throws an
it is
well
image,
and then another lens
enables the eye to form an image
of the image by rendering the
rays again parallel. These pa-
rallel *ays then enter the eye
just as the rays do in ordinary
vision.
A telescope, then, is a com-
bination of lenses.
•468. In the figure, for in-
stance, let A represent the first
or front lens, called the object-
glass, because it is the lens
nearest to the object viewed;
and let C represent the other
called the eye-lens, because it is
nearest the eye ; and let B repre-
sent the image of a distant arrow,
218 ASTRONOMY.
the beam of rays from which is seen falling on the object-
glass from the left. This beam is refracted, and we get an
inverted image at the focus of the object-glass, which is
also the focus of the eye-lens. Now, the rays leave the
eye-piece adapted for vision as they fall on the object-
glass, so the eye can use them as it could have u«ed them
if no telescope had been there.
4-69. What then has the telescope done? What is its
power? This question we will soon answer ; and, first,
as to what is called its illuminating power. The aperture
of the object-glass, that is to say, its diameter, being larger
than that of the pupil of our eye, its surface can collect more
rays than our pupil ; if this surface be a thousand times
greater than that of our pupil, for instance, // collects a
thousand times more light, and consequently the image
of a star formed at its focus has a thousand times more
light than the image thrown by the lens of our eye on
our retina.
But this is not quite true, because light is lost by
reflexion from the object-glass and by its passage through
it. If, then, we have two object-glasses of the same size,
one highly polished and the other less so, the illuminating
power of the former will be the greater.
47O. The magnifying power depends upon two things.
First, it depends upon the focal length ; because if we sup-
pose the focus to lie in the circumference of a circle having
its centre in the centre of the lens, the image will always
bear the same proportion to the circle. Suppose it covers
i°; it is evident that it will be larger in a circle of 12 feet
radius than in one of 12 inches. That is, it will be larger
in the case of a lens with 12 feet focal length than in one
of 12 inches' focal length.
4-71. Having this image at the focus, the magnifying
power of the eye-piece comes into play. This varies with
the eye-piece employed, the ratio of the focal length of
LIGHT. 219
the object-glass to that of the eye-piece giving its exact
amount ; that is to say, if the focus of the object-glass is
100 inches, and that of the eye-piece one inch, the tele-
scope will magnify 100 times. Bearing in mind that
what an astronomer wants is a good clear image of the
object observed, we shall at once recognise that magnify-
ing power depends upon the perfection of the image
thrown by the object-glass and upon the illuminating
power, of which we have already spoken. If the object-
glass does not perform its part properly, a slight magni-
fication blurs the image, and the telescope is useless.
Hence many large telescopes are inferior to much smaller
ones in the matter of magnifying power, although their
illuminating power is so much greater.
4-72. The eye-pieces used with the astronomical tele-
scope vary in form. The telescope made by Galileo,
similar in construction to the modern opera glass, was
furnished with a bi-concave eye-piece. As the action of the
eye-piece is to render the rays parallel, this eye-piece is
used between the object-glass and the focus, at a point
where its divergent action (Art. 462) corrects the conver-
gent action of the object-glass.
A convex eye-piece for the same reason is placed outside
the focus, as shown in Fig. 48.
Such eye-pieces, however, colour the light coming from
the image in the same way as the object-glass would
colour the light going to form the image, if its chromatic
aberration were not corrected.
4-73. It was discovered by Huyghens, however, that this
defect might be obviated in the case of the eye-piece by
employing two plano-convex lenses, the flat sides next the
eye, a larger one nearest the image, called the field-lens,
and a smaller one near the eye, called the eye-lens. This
construction is generally used, except for micrometers
(Art. 519), a name given to an eye-piece with spider-webs
220 ASTRONOMY.
in the focus of the eye-piece for measuring the sizes of the
different objects. In this case the flat sides are turned
away from the eye.
4.74. The telescope-tube keeps the object-glass and
the eye-piece in their proper positions, and the eye-piece
is furnished with a draw-tube, which allows its distance
from the object-glass to be varied.
LESSON XXXVIII; — THE TELESCOPE (continued}.
POWERS OF TELESCOPES OF DIFFERENT APERTURES.
LARGE TELESCOPES. METHODS OF MOUNTING THE
EQUATORIAL TELESCOPE.
4-75. Very many of the phenomena of the heavens may
be seen with a small telescope. In our climate a telescope
with an object-glass of six inches' aperture is probably
the size which will be found the most constantly useful ;
a larger aperture being frequently not only useless, but
hurtful. Still, 4i or 3} inches are useful apertures, and if
furnished with object-glasses, made of course by the best
makers, views of the sun, moon, planets, and double stars
may be obtained sufficiently striking to set many seriously
to work as amateur observers.
Thus, in the matter of double stars, a telescope of two
inches' aperture, with powers varying from 60 to 100, will
show the following stars double :—
Polaris. y Arietis. a Geminorum.
a Piscium. f Herculis. y Leonis.
fj. Draconis. £ Ursae Majoris. £ Cassiopeae.
A 4-inch aperture, powers 80120, reveals the duplicity
of— j3 Orionis. a Lyras. 8 Geminorum.
€ Hydrae. £ Ursae Majoris. o- Cassiopeas.
€ Bootis. y Ceti. * Draconis.
LI G PIT. 221
And a 6-inch, powers 240300 —
€ Arietis. X Ophiuchi. € Equulei.
5 Cygni. 20 Draconis. f Herculis.
32 Orionis. * Geminorum.
476, Observations should always be commenced with
the lowest power, or eye-piece, gradually increasing it until
the limit of the aperture, or of the atmospheric condition
at the time, is reached : the former being taken as equal
to the number of hundredths of inches which the diameter
of the object-glass contains. Thus, 3i-inch object-glass,
if really good, should bear a power of 375 on double stars
where light is no object ; the planets, the moon, &c. will
be best observed with a much lower power.
477. In the case of stars, owing to their immense dis-
tance, no increase in their size follows the application
of higher magnifiers. With planets this is different, each
increase of power increases the size of the image, and
therefore decreases its brilliancy, as the light is spread
over a larger area. Hence the magnifying power of a
good telescope is always much higher for stars than for
planets, although at the b^st it is always limited by the
state of the air at the tim? of observation.
4-78. It is always more or less dangerous to look at the
Sun directly with a telescope of any aperture above two
inches, as the dark glasses, without which the observer
would be at once blinded, are apt to melt and crack.
A diagonal reflector, however, which reflects an ex-
tremely small percentage of light to the eye, and by reason
of its prismatic form refracts the rest away from the tele-
scope, affords a very handy method of solar observation.
Care should be taken that the object-glass is properly
adjusted. This may be done by observing the image of a
large star out of focus. If the light be not equally dis-
tributed over the image, or the circles of light which are
222 ASTRONOMY.
always seen in a good telescope are not perfectly circular,
the telescope should be sent back to the optician for
adjustment.
479. The testing of a good glass refers to two different
qualities which it should possess. Its quality, as to
material and the fineness of its polish, should be such
that the maximum of light shall be transmitted. Its
quality as to the curves should be such that the rays
passing through every part of its area shall converge abso-
lutely to the same point, with a chromatic aberration
sufficient to surround objects with a faint dark blue
light.
480. To give an idea of the great accuracy with which
a fine object-glass refracts the light transmitted, we will
take for example an object-glass of 8 inches' aperture and
10 feet focal length, which, if a fine one, will separate the
components of y2 Andromedae, whose angular distance is
about half a second— that is, it will depict at its focus two
minute discs of light fairly separated, the distance of
whose centres, as above stated, is half a second. To come
at the value of this half-second, as measured on a scale of
inches and parts, we must consider the centre of the
object-glass to be the centre of a circle, whose radius is
the focal length of the object-glass. The focal value of a
degree of such a circle is 2*0944, or nearly 2^ inches ; of
a minute, "0349 of an inch ; of a second, '0005818, or -5$^
of an inch nearly ; of half a second, "0002909 inch, which
is little more than the fourth part of the one- thousandth
of an inch. Light from a fixed star passing through four
refracting surfaces, and half an inch or more in thickness of
glass, and filling 50 square inches of surface, and travelling
1 20 inches down the tube, is so accurately concentrated
at the focal point as to all pass through the smallest hole
that could be made with the most delicate needle-point
through a piece of fine paper. This requires a degree of
LIGHT. 223
accuracy in the figuring and polishing of the material of
the lenses almost inconceivable.
481. We have so far confined our attention to the
principles of the ordinary astronomical telescope, and we
have dealt with it in its simplest form. There are other
kinds ; the construction of some of which depends upon
reflection; that is to say, the light is reflected by a concave
mirror instead of being refracted by a lens ; but we need
not dwell upon them. Let us next inquire what the very
largest telescope really can do. The largest refractor —
as the refracting telescopes are called — in the world has
just been completed by Messrs. Cooke and Sons, English
opticians of great eminence. The object-glass is 25 inches
in diameter. Now, the pupil of our eye is J-th of an inch
in diameter : this object-glass, therefore, will grasp 15,000
times more light than the eye can : if used when the air
is pure, it should easily bear a power of 3,000 on the
Moon; in other words, the Moon will appear as it would
were it 3,000 times nearer to us, or at a distance ot
80 miles, instead of, roughly, 240,000; measuring from the
centres of the Earth and Moon, and not from their surfaces.
The largest reflector in the world has been constructed
by the late Earl of Rosse ; its mirror, or speculum, is six
feet in diameter, and its illuminating power is such that
it enables us to see, " as clearly as the heavens shine
to us on a cloudless evening, the details of a starry uni-
verse, stretching into space five hundred times further
than those depths at which we are accustomed to gaze
almost in oppressive silence."*
482. An astronomer wants telescopes for two kinds of
work : he wants to watch the heavenly bodies, and study
their physical constitution; and he wants to note their
actual places and relative positions; so that he mounts
or arranges his telescope in several different ways.
* Nichol.
224 ASTRONOMY.
483. For the first requirement it is only essential
that the instrument should be so arranged that it can
command every portion of the sky. This may be accom-
plished in various ways : the best method of accomplish-
ing it is shown in Plate XII., which represents an eight-
inch telescope, equatorially mounted— or, shortly, an
equatorial — that is, an instrument so mounted that a
heavenly body may be followed from rising to setting by
one continuous motion of the telescope, which motion
may be communicated by clockwork.
484. In this arrangement a strong iron pillar supports
a head-piece, in which is fixed the polar axis of the instru-
ment parallel to the axis of the Earth, which polar axis
is made to turn round once in twenty-four hours by the
clock shown to the right of the pillar.
485. It is obvious that a telescope attached to such an
axis will always move in a circle of declination, and that
a clock, carrying the telescope in one direction as fast as
the Earth is carrying the telescope from a heavenly body
in the opposite one, will keep the telescope fixed on the
object. It is inconvenient to attach the telescope directly
to the polar axis, as the range is then limited : it is
fixed, therefore, to a declination axis, placed above the
polar axis, and at right angles to it, as shown in the plate.
486. For the other kinds of work, telescopes, generally
of small power except in important observatories, are
mounted as altazimuths, transit-insti laments, tiansit-
circies, and zenith-sectors. These descriptions of
mounting, and their uses, will be described in Chap. VII.
Plate XII.
EIGHT-INCH EQUATORIAL TELESCOPE, WITH THE COOKE MOUNTING.
Q
LIGHT. 227
LESSON XXXIX,— THE SOLAR SPECTRUM. THE
SPECTROSCOPE. KIRCHHOF^S DISCOVERY. PHVSICAL
CONSTITUTION OF THE SUN.
487. A careful examination of the solar spectrum has
told us the secret of the enormous importance of solar
radiation (Art. 124). Not only may we liken the gloriously
coloured bands which we call the spectrum to the key-
board of an organ — each ray a note, each variation in
colour a variation in pitch— but as there are sounds in
nature which we cannot hear, so there are rays in the sun-
beam which we cannot see.
488. What we do see is a band of colour stretching
from red, through yellow, green, blue, violet, indigo, to
lavender, but at either end the spectrum is continued.
There are dark rays before we get to the red, and other
dark rays after we leave the lavender — the former heat
rays, the latter chemical rays ; and this accounts for the
threefold action of the sunbeam : heating power, lighting
power, and chemical power.
489. When a cool body, such as a poker, is heated in
the fire, the rays it first emits are entirely invisible, or
dark : if we looked at it through a prism, we should see
nothing, although we can easily perceive by the hand that
it is radiating heat. As it is more highly heated, the
radiation from the poker gradually increases, until it
becomes of a dull red colour, the first sign of incandes-
cence ; in addition to the dark rays it had previously
emitted, it now sends forth waves of red light, which a
prism will show at the red end of the spectrum : if we still
increase the heat and continue to look through the prism,
we find, added to the red, orange, then yellow, then green,
Q 2
228 ASTRONOMY.
then blue, indigo, and violet, and when the poker is white-
hot all the colours of the spectrum are present. If, after
this point has been reached, the substance allows of still
increased heating, it will give out with increasing in-
tensity the rays beyond the violet, until the glowing body
can rapidly act in forming chemical combinations, a
process which requires rays of the highest refrangibility
— the so-called chemical, actinic, or ultra-violet rays.
49O. We owe the discovery of the prismatic spectrum
to Sir Isaac Newton, but the beautiful colouring is but
one part of it. Dr. Wollaston in the year 1802 discovered
that there were dark lines crossing the spectrum in dif-
ferent places. These have been called Fraunhofer's
lines, as an eminent German optician of that name after-
wards mapped the plainest of them with great care : he
also discovered that there were similar lines in the spectra
of the stars. The explanation of these dark lines we owe
to Stokes, and more particularly to Kirchhoff. The law
which explains them was, however, first proved by Balfour
Stewart.
4-91. We shall observe the lines best if we make our
sunbeam pass through an instrument called a spectro-
scope, in which several prisms are mounted in a most
careful manner. We find the spectrum crossed at right
angles to its length by numerous dark lines — gaps—
which we may compare to silent notes on an organ.
Now if we light a match and observe its spectrum, we
find that it is continuous — that is, from red through the
whole gamut of colour to the visible limit of the violet :
there are no gaps, no silent notes, no dark lines, breaking
up the band.
Another experiment. Let us burn something which
does not burn white; some of the metals will answer GUI
purpose. We see at once by the brilliant colours that
fall upon our eye from the vivid flame that we have here
Plate XIII.
LIGHT. 231
something different. The prism tells us that the spectrum,
instead of being continuous as before, now consists of
two or three lines of light in different parts of the
spectrum, as if on an organ, instead of pressing down
all the keys, we but sounded one or two notes in the
bass, tenor, or treble.
Again, let us try still another experiment. Let us so
arrange our prism, that while a sunbeam is decomposed
by its upper portion, a beam proceeding from such a light-
source as sodium, iron, nickel, copper, or zinc, may be
decomposed by the lower one. We shall find in each
case, that when the bright lines of which the spectrum of
the metal consists flash before our eyes, they will occupy
absolutely the same positions in the lower spectrum as
some of the dark bands, the silent notes, do in the upper
solar one.
4-92. Here, then, is the germ of KirchhofFs discovery,
on which his hypothesis of the physical constitution of
the Sun is based ; and here is the secret of the recent
additions to our knowledge of the stars, for stars are
suns.
Vapours of metals, and gases, absorb those rays which
the same vapours of metals and gases themselves emit.
4-93. By experimenting in this manner, the following
facts have been established :—
I. — When solid or liquid bodies are incandescent, they
give out continuous spectra.
11. — When solid or liquid bodies reduced to a state of
gas, or any gas itself, burns, the spectrum con-
sists of bright lines only, and these bright lines
are different for different substances.
III. — \Vhen light from a solid or liquid passes through
a gas, the gas absorbs those particular rays of
light of which its own spectrum consists.
232 ASTRONOMY.
This third law is the one established by Kirchhoff in
1859.
4-94.. We are now in a position to inquire what has
become of those rays which the dark lines in the solar
spectrum tell us are wanting — those rays which were
arrested in their path, and prevented from bearing their
message to us. Before they left the regions of our incan-
descent Sun, they were arrested by those particular
metallic vapours and gases in his atmosphere, with which
they beat in unison ; and the assertion, that this and that
metal exists in a state of vapour in the Sun's atmosphere,
is based upon their non-arrival ; for so various and
constant are the positions of the bright bands in the
spectra we can observe here, and so entirely do they
correspond with certain dark bands of the spectrum of
the Sun, that it has been affirmed, that the chances
against the hypothesis being right are something like
300,000,000 to I.
4-95. So much for the Sun. Fraunhofer was the first
to apply this method to the stars ; and we have lately
reaped a rich harvest of facts, in the actual mapping down
of the spectra of several of the brightest stars, and the
examination, more or less cursory, of a very large number.
In all the plan of structure has been found to be the
same ; in all we find an atmosphere sifting out the rays
which beat in unison with the metallic and gaseous
vapours which it contains, and sending to us the residuum,
a broken spectrum abounding in dark spaces.
LIGHT. 233
LESSON XL. — IMPORTANCE OF THIS METHOD OF RE-
SEARCH. PHYSICAL CONSTITUTION OF THE STARS,
NEBULAE, MOON, AND PLANETS. CONSTRUCTION
OF THE SPECTROSCOPE. CELESTIAL PHOTOGRAPHY.
0
496. A few words will show the very great importance
of these facts from an astronomical point of view. They
tell us, that as the spectrum of the Sun's light contains dark
lines, the light is due to solid or liquid particles in a state
of great heat, or, as it is called, incandescence ', and that the
light given out by these particles is sifted, so to speak,
by its atmosphere, which consists of the vapours of the
substances incandescent in the photosphere. Further, as
the lines in the reversed spectra occupy the same positions
as the bright lines given out by the glowing particles
would do, and as we can by experimenting on the different
metals match many of the lines exactly, we can thus see
which light is thus abstracted, and what substance gives
out this light : having done this, we know what substances
(Art. 123) are burning in the Sun.
497. Again, it tells us that all the stars are, more or
less, like the Sun, for when they are shown in the same
manner we find nearly the same appearances ; and here
again in the same manner we can tell what substances are
burning in the stars (Art. 67).
498. The spectra of the nebula?, instead of resembling
that of the Sun and stars, — that is, showing a band of
colour with black lines across it, — consist of a few bright
lines merely.
499. On August 29, 1864, Mr. Huggins directed his
telescope, armed with the spectrum apparatus, to the
234 ASTRONOMY.
planetary nebula in Draco. At first he suspected that
some derangement of the instrument had taken place, for
no spectrum was seen, but only a short line of light,
perpendicular to the direction of dispersion. He found
that the light of this Nebula, unlike any other ex-
terrestrial light which had yet been subjected to prismatic
analysis, was not composed of light of different refrangi
bilities, as in the case of the Sun and stars, and it there-
fore could not form a spectrum. A great part of the light
from this Nebula is monochromatic, and was seen in the
spectroscope as a bright line. A more careful exami-
nation showed another line, narrower and much fainter, a
little more refrangible than the brightest line, and sepa-
rated from it by a dark interval. Beyond this again, at
about three times the distance of the second line, a third
exceedingly faint line was seen.
500. The strongest line coincides in position with the
brightest of the air lines. This line is due to nitrogen,
and occurs in the solar spectrum about midway between
b and F. The faintest of the lines of the Nebula coin-
cides with the line of hydrogen, corresponding to the line
F in the solar spectrum. The other bright line was a
little less refrangible than the strong line of barium.
501. Here, then, we have three little lines for ever
disposing of the notion that nebulae may be clusters
of stars. How trumpet -tongtied does such a fact speak
of the resources of modern science ! That nebulas are
masses of glowing gas is shown by the fact that their
light consists merely of a few bright lines.
An object-glass collects a beam of light which for ever
without such aid would have bathed the Earth invisibly
to mortal eye ; the beam is passed through a prism, and
in a moment we know that we have no longer to do
with glowing Suns enveloped in atmospheres enforcing
tribute from the rays which pass through them, but with
LIGHT.
235
something deprived of an atmosphere, and that something
a glowing mass of gas (Art. 96).
5O2. In our own system, that moonshine is but sun-
shine second-hand, and that the Moon has no sensible
236 ASTRONOMY.
atmosphere, is proved by the fact, that in the spectroscope
there is no difference, except in brilliancy, between the
two ; and that the planets have atmospheres is shown in
like manner, since in their light we find the same lines as
in the solar spectrum, with the addition of other lines due
to the absorption of their atmospheres.
5O3. In the frontispiece are given a representation of the
solar spectrum, two maps of stellar spectra, the spectrum
of the nebula 37, H iv., and the double line of sodium.
The latter is given to explain the coincidences referred to
in the next article, on which our knowledge of the sub-
stances present in the atmospheres of the Sun and stars
depends. The light given out by the vapour of sodium
consists only of the double line shown in the plate. A
black double line, in exactly the same position in the
spectrum, is seen in the spectra of the Sun, Aldebaran, and
a Orionis. Similarly, were we to observe the spectrum
of the vapour of iron in the same position as the 400 or
500 bright bands visible in this case, we should see co-
incident lines in the spectrum of the Sun. The feebleness
of the light of the stars does not permit all these lines to
be observed. It is seen in the plate that one of the bright
bands in the spectrum of the nebula is coincident with one
of the lines of nitrogen, and one with the hydrogen line.
5O4-. In the spectrum of a Orionis, among the eighty
lines observed and measured by Dr. Miller and Mr.
Huggins, no less than five cases of coincidence have
been detected ; that is to say, we have now evidence
— universally accepted in the case of the Sun — that
sodium, magnesium, calcium, iron, and bismuth are pre-
sent in the atmosphere of a Orionis.
5O5. The star spectroscope, Fig. 49, with which these
spectra have been observed, is attached to the eye end
of an equatorial. As the spectrum of the point which
the star forms at the focus is a line, the first thing done
LIGHT. 237
in the arrangement adopted is to turn this line into a
band, in order that the lines or breaks in the light may be
rendered visible.
The other parts of the arrangement are as follow : —
A plano-convex cylindrical lens, of about fourteen inches
focal length, is placed with its axial direction at right
angles to the direction of the slit, and at such a distance
jDefore the slit, within the converging pencils from the
object-glass, as to give exactly the necessary breadth to
the spectrum. Behind the slit, at a distance equal to its
focal length, is an achromatic lens of 4% inches focal
length. The dispersing portion of the apparatus consists
of two prisms of dense flint glass, each having a refracting
angle of 60°. The spectrum is viewed through a small
achromatic telescope, provided with proper adjustments,
and carried about a centre suitably adjusted to the posi-
tion of the prisms by a fine micrometer screw. This
measures to about the 2D\ffith part of the interval between
A and H of the solar spectrum. A small mirror attached
to the instrument receives the light, which is to be com-
pared directly with the star spectrum, and reflects it upon
a small prism placed in front of one half of the slit. This
light was usually obtained from the induction-spark taken
between electrodes of different metals, raised to incan-
descence by the passage of an induced electric current.
5O6. The spectroscope represented in Plate XIII. is
a very powerful one, made by Mr. Browning for Mr.
Gassiot.and was for some time employed at the Kew Obser-
vatory for mapping the solar spectrum. The light enters
at a narrow slit in the left-hand collimator, which is fur-
nished with an object-glass at the end next the prism, to
render the rays parallel before they enter the prisms. In
the passage through the prisms the ray is bent into a
circle, widening out as it goes, and in consequence enters
the telescope on the right of the drawing.
238 ASTRONOMY.
It is often convenient to employ what is termed a
direct- vis ion spectroscope — that is, one in which the light
enters and leaves the prisms in the same straight line.
How this is managed in the Herschel-Browning spectro-
scope, one of the best of its kind, may be gathered from
Fig. 50.
Fig- 50 —Path of the ray in the Herschel-Browning spectroscope.
5O7. In both telescopic and spectroscopic observations
the visible rays of light are used. The presence of the
chemical rays, however, enables photographs of the
brighter celestial objects to be taken, and celestial photo-
graphy, in the hands of Mr. De la Rue and Mr. Ruther-
ford, has been brought to a high state of perfection. The
method adopted is to place a sensitive plate in the focus
of a reflector, or refractor properly corrected for the actinic
rays, and then to enlarge this picture to the size required.
Mr. De la Rue's pictures of the Moon, some I J inches in
diameter, are of such perfection that they bear subse-
quent enlargement to 3 feet. These pictures are now
being used as a basis of a map of the Moon, 200 inches in
diameter. A picture of the Sun is now taken every fine
day at Kew, by a somewhat similar method ; and we may
hope fora wide increase of our knowledge of solar physics
from this source.
CHAPTER VII.
DETERMINATION OF THE APPARENT PLACES
OF THE HEAVENLY BODIES.
LESSON XLL— GEOMETRICAL PRINCIPLES. CIRCLE.
ANGLES. PLANE AND SPHERICAL TRIGONOMETRY.
SEXTANT. MICROMETER. THE ALTAZIMUTH AND
ITS ADJUSTMENTS.
508. That portion of our subject which deals with
apparent positions is based upon certain geometrical
principles, among which the properties of the circle are
the most important.
509. A circle is a figure bounded by a curved line, all
the points in which are the same distance from a point
within the circle called the centre. The curved line itself
is called the circumference ; a line from any part of the
circumference to the centre is called a radins ; and if we
prolong this line to the opposite point of the circumference
we get a diameter. Consequently, a diameter is equal to
two radii.
510. The circumference of every circle, large or small,
is divided into 360 parts, called degrees, which, as we
have before stated (Art. 159), are divided into minutes
240 ASTRONOMY.
and seconds, marked (') and ("), to distinguish them from
minutes and seconds of time, marked (m) and (8).
511. That part of the circumference intercepted by
any lines drawn from it to the centre is called an arc, and
the two lines which join at the centre inclose what is
called an angle, the angle in each case being measured
by the arc of the circumference of the circle intercepted.
512. The arc, and therefore the measured angle, will
contain the same number of degrees, however large or
small the circle may be — or, in other words, whatever be
the diameter. Each degree will, of course, be larger in a
large circle than in a small one, but the number of degrees
in the whole circumference will always remain the same ;
and therefore the angle at the centre will subtend the
same number of degrees, whatever be the radius of the
circle.
513. An angle of 90° is called a right angle, and there
are therefore four such angles at the centre of a circle.
The two lines which form a right angle are said to be at
right angles to each other. If we print a'T, for instance,
like this J_, we get two right angles, and the upright
stroke is called a perpendicular.
514-. When the opening of an angle is expressed by
the number of degrees of the arc of a circle it contains,
it is called the angular measure of the angle. Another
property of the circle is, that whatever be its size, the
diameter, and therefore the radius, always bears the same
proportion to the circumference. The circumference is a
little more than three times the diameter — more exactly
expressed in decimals, it is 3*14159 times the diameter;
in other words —
diam. X 3'HJ59 = circumference ;
and therefore
circumference -T- 3*14159 = diameter.
DETERM1NA TION OF POSITIONS, 241
For the sake of convenience, this number 3*14159 is
expressed by the Greek letter TT. When either the radius,
diameter, or circumference is known, we can easily find
the others.
515. We next come to the properties of triangles. A
triangle is a figure which contains three angles, and it is
therefore bounded by three sides. If all three sides are
on the same plane, the triangle is called a plane triangle;
but if they lie on the surface of a sphere, it is called a
spherical triangle, and the sides, as well as the angles,
may be expressed in angular measure ; as the angular
length of each side is the angle formed by its two ends at
the centre of the sphere. For instance, if we on a ter-
restrial globe draw lines connecting London, Dublin, and
Edinburgh, we shall have a spherical triangle, as the
Earth is a sphere; and we can express the opening of each
angle and the length of each side in degrees. WTe may
treat three stars on the celestial sphere in the same
manner. Each angle of a plane triangle is determined
as we have already seen ; and it is one of the properties
of a triangle that the three interior angles taken together
are equal to two right angles— that is, 180°. It is clear,
therefore, that if we know two of the angles, the third is
found by subtracting their sum from 180°.
Fig. 51. — Two triangles.
Here are two triangles, and they look very unlike ; but
there is one thing in which we have just seen they exactly
R
242 ASTRONOMY.
resemble each other. The angles a be in both are together
equal to two right angles. Now one is a right-angled
triangle, i.e. the angle b is a right angle, or an angle
that contains 90°; consequently, we know that the other
angles, a and r, are together equal to 90°; and therefore,
if we know how many degrees the angle a or c contains,
we know how many the other must contain.
Why are we so anxious to know about these angles ?
Let us see. Here are three more triangles —
B
g- 52- ~ Triangles u ith two equal sides and unequal bases.
apparently very unlike ; but still we have made the sides
ac, ad, ae, af, ag, ah, all equal. Now look at the
upper angles <?, and look at their bases B B' B" : where
the angle is widest, the base is longest ; where narrowest,
the base is shortest. There is an obvious connexion
between the angle and the side opposite to it, not only
in the three triangles, but in each one taken separately ;
and in fact, in any triangle, the sides are respectively
proportional, not actually to the opposite angles them-
selves, but to a certain ratio called the sine (Art. 516) of
these angles. Moreover, we can express any side of a
triangle in terms of the other sides and adjacent angles,
or of the other sides and the angle between them. In
short, that branch of mathematics called trigonometry
teaches us to investigate the properties of triangles so
closely that when in any triangle we have two angles,
and the length of one side, or one angle and the length
DETERMINATION OF POSITIONS. 243
of two sides, whether the triangle lie before us on a piece
of paper, or have at one of the angles a tower which we
cannot reach, or the Sun, or a star, we can find out all
about it.
516. Angles are studied by means of certain quantities
called trigonometrical ratios, which we give here, in
order that some terms which will be necessarily used in
the sequel may be understood.
m
**£• 53- — Trigonometrical ratios.
BAC may represent any angle, and PMis perpendicular
to AB. Then, for the angle A,
PM perpendicular) is called the sine of A
AP, 1S' hypothenusej (written sin. A}.
AM base ) is called the cosine of A
AP, hypothenuse,! (written cos. A}.
PM perpendicular i is called the tangent of A
AM, base, j (written tan. A).
AM base is called the co-tangent of
~FM, * 1S' perpendicular,' A (written cot. A).
AP hypothenuse | is called the secant of A
All, 1S' base, J (written sec. A).
AP hypothenuse \ is called the co-secant
PM, thatls> perpendicular,) (written cosec. A).
244 ASTRONOMY.
517. We shall return to the use of plane triangles in
astronomical methods in the next chapter. It may here be
remarked that the apparent places of the heavenly bodies
are referred to the celestial sphere by means of spherical
triangles, which are investigated by trigonometrical ratios,
in the same manner as plane triangles, and hence this
part of our subject is called Spherical Astronomy.
518. In all the instruments about to be described,
angles are measured by means of graduated arcs, or
circles attached to telescopes, the graduation being car-
ried sometimes to the hundredth part of a second of arc
by verniers or microscopes. It is of the last importance,
not only that the circle should be correctly graduated,
but that it should be correctly centred, — that is, that
the centre of movement should be also the centre of
graduation. To afford greater precision, spider webs, or
fine wires, are fixed in the focus of the telescope to point
out the exact centre of the field of view. An instrument
with the cross wires perfectly adjusted is said to be
correctly collimated.
519. In addition to the fixed wires, moveable ones
are sometimes employed, by which small angles may be
measured. An eye-piece so arranged is called a micro-
meter, or a micrometer eye-piece. The moveable wire
is fixed in a frame, set in motion by a screw, and the dis-
tance of this wire from the fixed central one is measured
by the number of revolutions and parts of a revolution
of this screw, each revolution being divided into a thou-
sand parts by a small circle outside the body of the
micrometer, which indicates or when the moveable and
central wire are coincident, and at each complete revo-
lution on either side of the latter. The angular value
of each revolution is determined by allowing an equa-
torial star to traverse the distance between the wires,
and turning the time taken into angular measurement.
xi y.
Portable Altazimuth Instrument.
DE TERM IN A TION OF POSITIONS. 247
Attached to the micrometer, or to the eye-piece which
carries it, is also a position-circle, divided into 360°; by
this the angle made by the line joining two stars, for
instance, with the direction of movement across the field
of view, is determined. The use of the position-circle
in double-star measurements is very important, and it is
in this way that their orbital motion has been deter-
mined. The micrometer wires, or the field of view, are
illuminated at night by means of a small lamp outside,
and a reflector inside, the telescope (see Plate XIV.).
520. If we require to measure simply the angular
distance of one celestial body from another, we employ
a sextant ; but generally speaking, what is to be deter-
mined is not merely the angular distance between two
bodies, but their apparent position either on the sphere
of observation or on the celestial sphere itself.
521. In the former case, — that is, when we wish to
determine positions on the visible portion of the sky, — we
employ what is termed an altitude and azimuth instru-
ment, or, shortly, an altazimuth; and if we know the
sidereal time, or, in other words, if we know the exact
part of the celestial sphere then on the meridian, we can
by calculation find out the right ascension and declina-
tion (Art. 328), referred to the celestial sphere, of the body
whose altitude and azimuth on the sphere of observation
we had instrumentally determined.
522. An altazimuth is an instrument with a vertical
central pillar supporting a horizontal axis. There are
two circles, one horizontal, in which is fitted a smaller
(ungraduated) circle with attached verniers fixed to the
central pillar, and revolving with it ; another, vertical, at
one end of the horizontal axis, and free to move in all
vertical planes. To this latter the telescope is fixed.
When the telescope is directed to the south point, the
reading of the horizontal circle is o° ; and when the
248 A
telescope is directed to the zenith, the reading of the ver-
tical circle is o°. Consequently, if we direct the telescope to
any particular star, one circle gives the zenith distance of
the star (or its altitude) ; the other gives its azimuth. If
we fix or clamp the telescope to the vertical circle, we can
turn the axis which carries both round, and observe all
stars having the same altitude, and the horizontal circle
will show their azimuths ; if we clamp the axis to the
horizontal circle, we can move the telescope so as to
make it travel along a vertical circle, and the circle
attached to the telescope will give us the zenith distances
of the stars (or the altitude), which, in this case, will lie in
two azimuths 180° apart. A portable altazimuth is repre-
sented in Plate XIV., the various parts of which will be
easily recognised from the foregoing description.
523. To make an observation with the altazimuth,
we must first assure ourselves that the instrument itself
is in perfect adjustment — that is, that the circles are
truly graduated and centred (Art. 518), and that there
is no error of collimation in the telescope. This done,
it must be perfectly levelled, so that the vertical circle
is in all positions truly vertical, and the horizontal circle
truly horizontal. Next, we must know the exact readings
of the verniers of the azimuth circle when the telescope
is in the meridian, and the exact readings of the verniers
of the vertical circle when the telescope points to the
zenith. This done, we may point the telescope to the
body to be observed, bring it to the cross wires visible
in the field of view, and note the exact time. The verniers
on the two circles are then read, and from the mean of
them the instrumental altitude and azimuth are deter-
mined. The observation should then be repeated with
the telescope on the opposite side of the central pillar, as
by this means some of the instrumental errors are got
rid of.
DETERMINA T/ON OF POSITIONS. 249
LESSON XLII. — THE TRANSIT CIRCLE AND ITS AD-
JUSTMENTS. PRINCIPLES OF ITS USE. METHODS
OF TAKING TRANSITS. THE CHRONOGRAPH. THE
EQUATORIAL.
524. When we wish to determine directly the position
of a celestial body on the celestial sphere itself, a transit
circle is almost exclusively used This instrument con-
sists of a telescope moveable in the plane of the meridian,
being supported on two pillars, east and west, by means of
a horizontal axis. The ends of the horizontal axis are of
exactly equal size, and move in pieces, which, from their
shape, are called Y s- When the instrument is in perfect
adjustment, the line of collimation of the telescope is at
right angles to the horizontal axis, the axis is exactly
horizontal, and its ends are due east and west. Under
these conditions, the telescope describes a great circle of
the heavens passing through the north and south points
and the celestial pole ; in other words, the telescope in all
positions points to some part of the meridian of the place.
On one side of the telescope is fixed a circle, which is
read by microscopes fixed to one of the supporting pillars.
The cross wires in the eye-piece of the telescope enable
us to determine the exact moment of sidereal time at
which the meridian is crossed : this time is, in fact, the
right ascension of the object. The circle attached shows
us its distance from the celestial equator : this is its decli-
nation. So by one observation, if the clock is right, if
the instrument be perfectly adjusted, and if the circle be
correctly divided, we get both co-ordinates.
In Plate XV. is given a perspective view of the great
250 ASTRONOMY.
transit circle at Greenwich Observatory, designed by the
present Astronomer Royal, Mr. Airy. It consists of two
massive stone pillars, supporting the ends of the horizontal
axis of the telescope, which rest on Y s, as shown in
the case of one of the pivots in the drawing. Attached
to the cube of the telescope (to which the two side-pieces,
the eye-piece end and object-glass end, are screwed) are
two circles. The one to the right is graduated, and is
read by microscopes pierced through the right-hand pillar ;
the eye-pieces of these microscopes are visible to the right
of the drawing. The other circle is used to fix the tele-
scope, or to give it a slow motion, by means of a long
handle, which the observer holds in his hand. The eye-
piece is armed with a micrometer, with nine equidistant
vertical wires and two horizontal ones.
The wheels and counterpoises at the top of the view
are to facilitate the raising of the telescope when the
collimators, both of which are on a level with the centre
of the telescope — one to the north and one to the south
— are examined.
525. As we have already seen (Art. 329), a celestial meri-
dian is nothing but the extension of a terrestrial one; and as
the latter passes through the poles of the Earth, the former
will pass through the poles of the celestial sphere : conse-
quently, in England the northern celestial pole will lie
somewhere in the plane of the meridian. If the position
of the pole were exactly marked by the pole-star, that
star would remain immoveable in the meridian ; and when
a celestial body, the position of which we wished to
determine, was also in the meridian, if we adjusted the
circle so that it read o° when the telescope pointed to
the pole, all we should have to do to determine the north
polar distance of the body would be to point the tele-
scope to it, and see the angular distance shown by the
circle.
Piate XY.
Perspective View of the Transit Circle at Greenwich.
DE TERMINA TION OF POSITIONS. 25 3
526. But as the pole-star does not exactly mark the
position, we have to adopt some other method. We
observe the zenith distance (Art. 329) of a circumpolar
star when it passes over the meridian above the pole, and
also when it passes below it, and it is evident that if the
observations are perfectly made, half the sum of these
zenith distances wiH give the zenith distance of the celestial
pole itself. When we have found the position of the
celestial pole, we can determine the position of the
celestial equator, which we know is exactly 90° away from
it. As we already know the zenith distance of the celestial
pole, the difference between this distance and 90° gives
us the zenith-distance of the equator. Here, then, we
have three points from which with our transit circle we
can measure angular distances : —
I. From the zenith,
II. From the celestial pole,
I 1 1. From the celestial equator,
and we may add,
IV. From the horizon,
as the horizon is 90° from the zenith. Any of these dis-
tances can be easily turned into any other.
527. In this way, then, if we reckon from, or turn our
measures into distances from, the celestial equator, we get
in the heavens the equivalent of terrestrial latitude. But
this is not enough : as we saw in the case of the Earth
(Art. 161) — a thousand places on the Earth may have
the same latitude — we want what is called another co-
ordinate to fix their position. On the Earth we get
this other co-ordinate by reckoning from the meridian
which passes through the centre of the transit circle at
254 ASTRONOMY.
Greenwich, which meridian passes through all places,
whatever their latitude, north or south, which have the
same longitude as Greenwich.
So in the heavens we reckon from the position oc-
cupied by the Sun at the vernal equinox. The astronomer
not only has a telescope and a circle, but, as we have
seen (Art. 425), he has a sidereal clock, adjusted to
the apparent movement of the stars, actually to the
Earth's rotation. On its dial are marked 24 hours.
The time shown by this clock is called sidereal, or star
time, and is so regulated that the exact interval between
two successive passages of the same star over the meri-
dian of the same place is divided into twenty-four sidereal
hours, these into sixty sidereal minutes, and so on; and
this time is reckoned, not from any actual star, but
from the point in the heavens called " the first point
of Aries? which we have mentioned ; when that point
is on the meridian of any place the sidereal clock shows
oh. om. os., and then it goes on indicating the twenty-
four sidereal hours till the same point comes on the
meridian again.
528. Now it follows, that as right ascension and
sidereal time are both reckoned from the first point of
Aries, a sidereal clock at any place will denote the right
ascension of the celestial meridian visible in the transit
circle at that moment ; and if we at the same moment,
by means of the circle, note how far any celestial
body is from the celestial equator, we shall know both
its right ascension and declination, and its place in
the heavens will be determined : that is to say, the Earth
itself, by its rotation, performs the most difficult part of
the task for us, and every star will in turn be brought
into the meridian of our place of observation ; all we
have to do is to note its angular distance either from the
zenith or from the celestial equator, and note the sidereal
DETERMINATION OF POSITIONS. 255
time : one enables us to determine, or actually gives us,
its declination ; the other gives us its right ascension.
529. Of course, the method which is good for deter-
mining the exact place of a single heavenly body is good
for mapping the whole heavens, and in this manner the
position of each body has been determined, until the
whole celestial sphere has been mapped out, the right
ascension and declination of every object having been
determined.
The most important of the catalogues in which these
positions are contained is due to the German astronomer
Argelander. This catalogue contains the positions of
upwards of 324,000 stars, from N. Decl. 90° to S. Decl. 2°.
Bessel also has published a catalogue of upwards of
32,000 stars. The Astronomer Royal and the British
Association have also published similar lists. There are
also catalogues dealing with double stars and variable
stars exclusively.
530. In order that the angular distance from the zenith,
and the time of meridian passage, may be correctly deter-
mined, observations of the utmost delicacy are required.
531. The circle of the Greenwich transit, for instance,
is read in six different parts of the limb at each obser-
vation by the microscopes, the eye -pieces of which are
shown in Plate XV., and the recorded zenith distance is
the mean of these readings.
The other co-ordinate, — that is, the right ascension, —
is obtained with equal care. The transit of the star is
watched over nine equidistant wires, in the micrometer
eye-piece (called in this case a transit eye-piece), the
middle one being exactly in the axis of the telescope.
The following table of some objects observed at Greenwich
on Aug. 7, 1856, will show how the observation made
at this central wire is controlled and corrected by the
observations made at the other wires on either side of it.
ASTROXOAfY.
NAME OF
OBJECT.
Seconds of Transit over the Wires.
Concluded
Transit
over the
Centre Wire.
I.
II.
III
IV.
V.
VI.
VII.
VIII
IX.
13 Lyrae . .
s
s.
S.
3'o
s.
68
s.
.4-8
s.
22 '0
s.
25 '9
s.
29-7
s.
33 5
h. m. s.
18 50. 14*34
K Cygni . .
407
45 '3
49-8
54-6
58-4
9-2
3'fi
4'4
15'6
I2'8
10 '6
21-8
i7'5
13-8
24-9
22 'O
,6-7
28 'o
267
19-7
31'"
19. 13. 3'58
19- 16. 4'48
19- 20. 15-48
X3 Sagittarii
B. A C. 6666
493
59 '9
52-4
3 *
55 5
6'2
S Cygni . .
55 'o
59 '4
3 7
7-8
16'8
25 2
29-7
34 'o
38-2
19-37- 16'57i
c * Cygni
Neptune. .
'
57-8
2'I
6'4
108
19'4
1T5
27-9
25'3
32-3
39 o
366
40-9
19- 37- 19'28j
23 23- 11'52
532. There are two methods of observing the time of
transit over a wire, one called the eye and ear method,
the other the galvanic method. In the former, the
observer, taking his time from the sidereal clock, which
is always close to the transit circle, listens to the beats
and estimates at what interval between each beat the
star passes behind each wire. An experienced observer
in this manner mentally divides a second of time into
ten equal parts with no great effort.
533. In the second method a barrel covered with paper
is made to revolve at an equal rate of speed. By mean*,
of a galvanic current, a pricker attached to the keeper of
an electro magnet is made at each beat of the sidereal
clock to make a puncture on the revolving barrel. The
pricker is carried along the barrel, so that the line of
punctures forms a spiral, the pricks being about half an
inch apart. Here then we have the flow of time fairly
recorded on the barrel. At the beginning of each minute
the clock fails to send the current, so that there is no
DETERMINATION OF POSITIONS. 275
confusion. What the clock does regularly at each beat
the observer does when a star crosses the wires of his
transit eye-piece. He presses a spring, and an additional
current at once makes a puncture on the barrel. The
time at which the transit of each wire has been effected
is estimated from the position the additional puncture
occupies between the punctures made by the clock at
each second.
534-. By this method, which is also termed the
chronographic method, the apparatus used being called
a chronograph, the observer is enabled to confine his
attention to the star, and after observing with the tele-
scope can at leisure make the necessary notes on the
punctured paper, which is taken off the barrel when filled,
and bound up as a permanent record.
535. With the transit circle the position of a body in
the celestial sphere can only be determined when that
object is on the meridian. The equatorial enables this to
be done, on the other hand, in every part of the sky,
though not with such extreme precision. The object is
brought to the cross wires of the micrometer eye-piece,
and the declination circle at once shows the declination
of the object. The right ascension is determined as
follows : — At the lower end of the polar axis is a circle
.divided into the 24 hours of right ascension. This circle
is not fixed. Flush with the graduation are two verniers ;
the upper one fixed to the stand, the lower one move-
able with the telescope. The fixed vernier shows the
position occupied by the telescope, and therefore by the
moveable vernier, when the telescope is exactly in the
meridian. Prior to the observation, therefore, the circle
is adjusted so that the local sidereal time, or, in other
words, the right ascension of the part of the celestial
sphere in the meridian, is brought to the fixed vernier.
The circle is then carried by the clockwork of the instru-
S
258 ASTRONOMY.
ment, and when the cross wires of the telescope are
adjusted on the object, the moveable vernier shows its
right ascension on the same circle.
LESSON XLIII. — CORRECTIONS APPLIED TO OBSERVED
PLACES. INSTRUMENTAL AND CLOCK ERRORS.
CORRECTIONS FOR REFRACTION AND ABERRATION.
CORRECTIONS FOR PARALLAX. CORRECTIONS FOR
LUNI-SOLAR PRECESSION. CHANGE OF EQUATORIAL
INTO ECLIPTIC CO-ORDINATES.
536. After the astronomer has made his observations
of a heavenly body — and has freed them from instru-
mental and clock errors, if his telescope is not perfectly
levelled or collimated, or his circle is not perfectly centred,
or if the clock is either fast or slow — he has obtained
what is termed the observed or apparent place. This,
however, is worth very little : he must, in order to obtain
its true place, as seen from his place of observation, apply
other corrections rendered necessary by certain properties
of light. These properties have been before referred to
in Arts. 450 and 451, and are termed the refraction and
aberration of light. Refraction causes a heavenly body
to appear higher the nearer it is to the horizon ; in the
zenith its action is nil ; near the horizon it is very decided,
so decided that at sunset, for instance, the sun appears
above the horizon after it has actually sunk below it.
It will be seen, therefore, that refraction depends only
upon the altitude of the body on the sphere of obser-
vation.
537. The correction for refraction is applied, therefore,
by means of some such table as the following : —
DETERMINA TION OF POSITIONS. 259
TABLE OF REFRACTIONS.
Apparent
Altitude.
Mean
Refraction.
Apparent
Altitude.
Mean
Refraction.
o /
/ 11
o /
/ n
0 O
34 54
11 0
4 49
o 20
30 52
12 O
4 25
o 40
27 23
13 o
4 5
I 0
24 25
14 o
3 47
I 30
20 51
15 o
3 32
2 0
18 9
20 0
2 37
2 30
16 i
25 o
2 3
3 o
14 15
30 o
i 40
3 30
12 48
35 o
I 22
4 o
ii 39
40 o
I 9
5 o
9 47
45 °
o. 58
6 o
8 23
50 o
o 48
7 o
7 20
60 o
o 33
8 o
6 30
70 o
O 21
9 °
5 49
80 o
O IO
IO 0
5 16
90 o
O O
538. This table will give a rough idea of the correc-
tion applied ; in practice, the corrections are in turn
corrected according to the densities of the air at the time
of observation. In the case of the transit circle, or altazi-
muth, the correction for refraction is applied by merely
reducing the observed zenith distance by the amount
shown in the refraction table.
S 2
260 ASTRONOMY.
539. The aberration results from the fact that the
observer's telescope carried round by the Earth's annual
motion round the Sun must always be pointed a little in
advance of the star (Art. 45 i), in order, as it were, to catch
the ray of light. Hence the star's aberration place will be
different from its real place, and as the Earth travels round
the Sun, and the telescope is carried round with it always
EABTH5 WAY
XT- 54- — Annual change of a Star's position, due to Aberration : abed, the
Earth, in different parts of its orbit ; a'b'c'd', the corresponding Aberration
places of the Star, varying from 'the true place in the direction of the
Earth's motion at the time.
pointed ahead of the star's place, the aberration place
revolves round the real place exactly as the Earth (if its
orbit be supposed circular) would be seen to revolve round
the Sun, as seen from the star : the aberration places of
all stars, in fact, describe circles parallel to the plane of
the Earth's orbit — if the star lie at the pole of the ecliptic
the circle will appear as one : the aberration place of a
star in the ecliptic will oscillate backwards and forwards,
as we are in the plane of the circle ; that of one in a
middle celestial latitude will appear to describe an ellipse.
The diameter of the circle, the major axis of the ellipse,
and the amount of oscillation, will all be equal ; but the
minor axes of the ellipses described by the stars in middle
latitudes will increase from the equator to the pole. The
invariable quantity is 20^4451, and is termed the constant
of aberration. It expresses, as we have seen, the relative
velocities of light and of the Earth in her orbit. It is
DETERMINA TION OF POSITIONS. 261
determined by the following proportion, bearing in mind
that the 360° of the Earth's orbit are passed over in 365 J
days, and that light takes 8m. i8s. to come from the Sun :
Days. m. s. ° "
3654 : 8 18 :: 360 : 20.45
The mode in which the correction for aberration is
applied may be gathered from Fig. 55.
Fig. 55.— *, the Star's true place ; s', the Aberration place.
540. The direction of the Earth's motion in its orbit,
called the Earth's Way, referred to the ecliptic, is always
90° behind the Sun's position in the ecliptic at the time ;
therefore the aberration place of the star will lie on the
great circle passing through the star and the spot in the
ecliptic lying 90° behind the Sun.
541. Observations of the celestial bodies near the
Earth, such as the Moon and some of the planets, when
made at different places on the Earth's surface, and cor-
rected as we have indicated, do not give the same result,
as their position on the celestial sphere appears different to
observers on different points of the Earth's surface. This
?62
ASTRONOMY.
effect will be readily understood by changing our position
with regard to any near object, and observing it projected
on different backgrounds in the landscape ; the nearer we
are to the object the more will its position appear to
change.
542. To get rid of these discordances, the observations
are further reduced and corrected to what they would
have been had they been made at the centre of the Earth.
Fig. 56.— Parallax of a heavenly body.
This is called applying the correction for parallax.
Parallax is the angle under which a line drawn from the
observer to the centre of the Earth would appear at the
body of which observations are being made. When the
body is in the zenith of an observer, therefore, its parallax
is nil i it is greatest when the body is on the horizon.
This is termed the horizontal parallax. The line is
always equal to the radius of the Earth, but being seen
more or less obliquely, the parallax varies accordingly.
DETERMINATION OF POSITIONS. 263
543. The value of the correction for parallax is found
as follows: — In Fig. 56, let s be a star, z the zenith, o an
observer, c the centre of the Earth, and h the horizon. The
angle o s c is the parallax of the star s. It is one of the
properties of triangles that the sides are proportional to
the sines of the opposite angles : in the triangle o s c, for
instance, we have •
Sin. osc : sin. co s :: oc : cs.
54-4. The angle osc is the parallax of the star ; let
us therefore call it p. The angle cos = 1 80° — the
zenith distance, which we will write shortly, 1 80° — z ; oc
is the Earth's radius, which may be called r, and cs
the star's distance, which we will call D; so the equation
takes this form : —
Sin./ : sin. (180° — z) : : r : D.
Or (since the sine of 180° — z is equal to the sine of z),
Sin./ = -= sin. z (i).
It is seen that in the case of horizontal parallax sin. z
becomes equal to i, so that
Sin. P - j) (2).
As will be seen in the next chapter, this formula en-
ables us to find the distances of all the heavenly bodies
that are near enough to have any sensible parallax.
545. From what has been said it will be seen that on
the celestial sphere the positions of the heavenly bodies
are determined by means of either of two fundamental
planes — one of them the plane of the ecliptic, the other
the plane of the Earth's equator ; and that one of the
intersections of these two planes, — that, namely, occupied
264 ASTRONOMY.
by the Sun at the vernal equinox, called the first point of
Aries, written shortly, r. — is the start-point of one of the
co-ordinates. Thus :
Declination is reckoned N. or S. of the plane of the
earth's equator.
Celestial latitude is reckoned N. or S. of the plane of
the ecliptic.
Right ascension and celestial longitude are both
reckoned from the first point of
Aries, which marks one of the
two intersections of the two funda-
mental planes.
54-6. Now one plane marks the plane of the Earth's
yearly motion round the Sun, the other marks the plane of
the Earth's daily rotation. If therefore these are change-
less, a position once determined will be determined once
for all ; but if either the plane of the Earth's yearly
motion or the direction of the inclination of the Earth's
axis change, then the point of intersection will vary, and
corrections will be necessary.
54-7. We stated in Art. 168 that, roughly speaking, the
Earth's axis was always pointed in the same direction, or
remained parallel to itself ; but strictly speaking this is not
the case. It is now known that the pole of the Earth is
constantly changing its position, and revolves round the
pole of the ecliptic in 24,450 years, so that the pole-star
of to-day will not be the pole-star 3,000 years hence.
54-8. Now a very important fact follows from this ; as
the Earth's axis changes, the plane of the equator changes
with it, and so that each succeeding vernal equinox hap-
pens a little earlier than it otherwise would do. This
is called the precession of the equinoxes (because the
equinox seems to move backwards, or from left to right,
so as to meet the Sun earlier), or Inni-solar precession.
DETERMINA TION OF POSITIONS. 26$
The result of this is, that could we see the stars behind
the Sun, we should see different ones at each successive
equinox. In the time of Hipparchus — 2,000 years ago —
the Sun at the vernal equinox was in the constellation
Aries j now-a-days it is in the constellation/*/^^ (Art. 361).
549. The plane of the ecliptic is also subject to
variation. This is termed the secular variation of the
obliquity of the ecliptic.
550. Of these changes, the luni-solar precession is the
most important ; it causes the point of intersection of the
two fundamental planes to recede S°"37S72 annually, the
general precession amounting to $o"2H2g. To this is
due the difference in length between the sidereal and
tropical years (Art. 439).
551. The cause of these changes, as will be seen in
Chap. IX., is the attraction exercised by the Sun, Moon,
and planets upon the protuberant equatorial portions
of our Earth. The effect is to render both latitudes
and longitudes, and right ascensions and declinations
variable. Hence the observed position of a heavenly
body to-day will not be the position occupied last year,
or to be occupied next year, and apparent positions have
to be corrected, to bring them to some common epoch —
such as 1800, 1850, 1880, &c., so that they may be strictly
comparable.
552. As was pointed out in Lesson XXIX., astronomers
not only deal with positions on the celestial sphere de-
termined by right ascension and declination, but they
require to look at it, as it were, from the ecliptic point of
view, and to know the distances of bodies from that plane,
still using the same first point of Aries, as in RA. These
co-ordinates are termed celestial latitude and longitude ;
they are not determined from observation, but are calcu-
lated from the true RA. and Decl. by means of spherical
trigonometry.
266
ASTRONOMY.
553. The first thing to be done is to determine what
is called the obliquity of the ecliptic (written eo) — that
is, the angle the ecliptic makes with the equator. This is
done by observing the declination of the Sun at the two
solstices, at which times the declination is exactly equal
to the obliquity. At the summer solstice the Sun is
north of the equator, at the winter solstice south, by the
exact amount of the obliquity.
Pig 57. — Transformation of Equatorial and Ecliptic Co-ordinates.
554-. When a> is known, to transform RA. and Decl.
into lat. and long, we proceed as follows : — In Fig. 57,
let s represent the body whose right ascension and decli-
nation are known ; T the sign for the first point of Aries,
L part of the equator, so that r L = the right ascension
of the body, as RA. is measured along the equator fromT ;
sL part of a meridian of declination, and therefore the
declination of the body; the angle Z'rZ the obliquity of
the ecliptic; and Z'r the position of the ecliptic with
regard to the equator.
This is what we know.
What we want to know are, rZ', the longitude, and
sL', the latitude. Let us call the right ascension RA.,
DETERMINA TION OF POSITIONS. 267,
the declination 6, the longitude /, the latitude X, and the
obliquity &>.
Before we can determine / and X we must find T s and
the angle srL. The triangle sL T is right-angled at Z, as
the meridians of RA. cross the equator at right-angles ;
by a formula of spherical trigonometry we have
cos. rs — cos. RA. cos. 8 (i).
From this is determined T s. Again, we have
cot. srL = sin. RA. cot. 8 (2).
From this is determined the angle sr L.
In the right-angled triangle sr L', in which we want to
know sL' and r Z/, we now know r s ; the angle at Z',
which is a right angle ; and the angle s r L', which =
srL — o>, or the angle L'rL. We get the sine of X
from the following equation :—
sin. X = sin.Tjsin.(jrZ — o>) . . ... (3).
and we get the tan. of / from this : —
tan. / = tan.rjcos. (srL — <•>} , . . (4).
The actual latitude and longitude are then found from a
table of sines and tangents.
268 ASTRONOMY.
LESSON XLIV. — SUMMARY OF THE METHODS BY
WHICH TRUE POSITIONS OF THE HEAVENLY BODIES
ARE OBTAINED. USE THAT IS MADE OF THESE
POSITIONS. DETERMINATION OF TIME : OF LATI-
TUDE : OF LONGITUDE.
555. What has hitherto been said in this chapter may
be summarized as follows : —
1. The astronomer, to make observations on his sphere
of observation merely, makes use principally either
of a sextant or an altazimuth. The positions of a
celestial body thus determined may by calculation be
referred to the celestial sphere itself, and its RA.
and Decl. determined.
2. Observations of a celestial body with regard to the
celestial sphere itself are principally made by means
of a transit circle, or an equatorial, by which both
apparent right ascension and declination may be
directly determined.
3. In all observations the instrumental and clock errors
are carefully obviated, or corrected.
4. Besides the instrumental and clock errors there are
others — refraction and aberration, which depend upon
the finite velocity of light, and its refraction by our
atmosphere. These also must be corrected.
5. Besides these, another error, parallax, results from the
observer's position on the Earth's surface. This is
corrected by reducing all observations to the centre
of the Earth.
6. There are still other errors depending upon the
change of the intersection of the two planes to which
DETERMINA TION OF POSITIONS. 269
all measurements are referred. These are got rid of
by reducing all observations to a point of time (as
parallax was got rid of by reducing them to a point
of space — the centre of the Earth). This is accom-
plished by fixing upon the position of the intersection
at a given epoch, such as 1800, 1880, &c., and re-
ducing all observations to what they would have been
had they been made at such epoch, or what they will
be when made at such epoch.
7. The right ascension and declination are then easily
converted by calculation into celestial longitude and
latitude if required.
556. By means of observations freed from all these
errors, extending over centuries, astronomers have been
able to determine the positions of all the stars, and to
map the heavens with the greatest accuracy. They have
also discovered the proper motions (Art. 43) of some
among the stars.
557. Similarly they have been able to investigate the
motions of the bodies of our system so accurately, that
they have discovered the laws of their motions. This
knowledge enables them to predict their exact positions
for many years in advance, and each of the first-rate Powers
publishes beforehand, for the use of travellers and navi-
gators, an almanac, or ephemeris, in which are given, with
most minute accuracy, the positions of the principal
stars, the planets, and the Sun from day to day, and
the positions of the Moon from hour to hour. Such are
the English and American " Nautical Almanacs," the
French " Connaissance des Temps," the German " Ber-
liner Jahrbuch." These positions enable us to determine
I. Time. II. Latitude. III. Longitude.
558. When time only is required, a transit instrument
is employed — that is, a simple telescope mounted like the
transit circle, but without the circle, or with only a
270 ASTRONOMY.
small one : the transits of stars, the right ascension of
which has been already determined with great accuracy
by transit circles, in fixed observatories, being observed.
This gives us the local sidereal time ; it may, if neces-
sary, be converted into mean solar time by the rule in
Art. 427.
559. As we have seen in a previous Lesson (XL), all
that we require to determine our position on the Earth's
surface is to learn the latitude and longitude. The deter-
mination of the former co-ordinate in a fixed observatory
is an easy matter, if proper instruments be at hand. For
instance : half the sum of the altitudes (corrected for
refraction) of a circumpolar star, at upper and lower
culminations, even if its position is unknown, will give
us the elevation of the pole, and therefore the latitude
of the place. Or, if we determine the zenith distance
of a star, the declination of which has been accurately
determined, we determine the latitude. For as declina-
tion is referred to the plane of the celestial equator
prolonged to the stars, it is the exact equivalent of
terrestrial latitude. If a star of o° declination is observed
exactly in the zenith, it is known that the position of the
observer is on the equator ; if the declination of a star in
the zenith is known to be 45°, then our latitude is 45° ; and
if a star of, say, N. 39° passes 10" to the north of our zenith,
then our latitude is 38° 59' 50", and so on.
560. To determine latitude, then, all that is required is
to know either the elevation of the pole or the zenith
pistance of a heavenly body whose declination is known.
561. On board ship, and in the case of explorers, the
problem is for the most part limited to determining the
meridian altitude of the Sun or Moon, as the sextant
only can be employed. Suppose such an observation to
give the altitude as 39° from the south point of the hori-
zon— that is, 61° zenith distance — and that the Nautical
DETERMINA TION OF POSITIONS. 271
Almanac gives Its declination on that day as 12° south ; if
we were in lat. I2°S. the Sun should be overhead, and its
zenith distance would be nil ; as it is 6 1° to the south, we
are 61° to the north of 12° S., or in N. lat. 49°. So, if we
observe the meridian altitude as 10° from the north point
of the horizon, or zenith distance 80°, and the Nautical
Almanac gives the declination at the time as 20° N.,
our position will be in 60° S. latitude.
562. Next, as to longitude. Longitude is in fact time,
and difference of longitude is the difference of the times
at which the Sun crosses any two meridians, the twenty-
four hours solar mean time being distributed among the
360° of longitude, so that I hour =15°, and so on.
563. There are several ways of determining longitude
employed in fixed observatories : the most convenient one
consists in electrically connecting the two stations, the
difference of longitude between which is being sought
and observing the transit of the same stars at each. Thus
the transits at station A are recorded on the chronograph
at stations A and B, and the transits at station B are
similarly recorded at B and A ; from both chronographs
the interval between the times of transit is accurately
recorded in sidereal time, and the mean of all the differences
converted into mean solar time gives the difference of
longitude.
564-. At sea, the problem, which consists of finding the
difference between the local and Greenwich time, is solved
generally by one of three methods. The first of these is
to carry Greenwich time with the ship by means of very
accurate chronometers, and whenever the local time is
determined (which is done at noon by observing, with the
aid of a sextant, when the Sun is at the highest point of
its path,) noting the difference between the local time
and the chronometer. If, for instance, when noon is
thus determined, the chronometer shows three hours at
272 ASTRONOMY.
Greenwich, the ship is three hours or 45° to the west of
Greenwich ; in other words, in long. 45° W.
565. The second method consists in making use of the
heavens as a dial-plate, and of the Moon as the hand.
In the Nautical Almanac the distances of the Moon
from the stars in her course are given for every third
hour in Greenwich time. These distances are to be cor-
rected for refraction and parallax. The sailor, therefore,
observes the Moon's distance from the stars given in the
almanac and corrects his observation for refraction and
parallax ; referring to the Nautical Almanac, he sees
the time at Greenwich, at which the distance is the same
as that given by his Observation, and knowing the local
time (from day observations) at the instant at which his
observation was made, the difference of time, or longitude,
is readily found.
566. A third method (scarcely, however, available at
sea) is to watch the eclipses of Jupiter's satellites, which
are visible all over the Earth, whenever seen, at the same
instant ; the instant at which they actually take place
being carefully stated in the Nautical Almanac in Green-
wich time. If, therefore, one be observed, and the local
time be known, the difference of time or longitude is also
known.
CHAPTER VIII.
DETERMINATION OF THE REAL DISTANCES AND
DIMENSIONS OF THE HEAVENLY BODIES.
LESSON XLV.— -MEASUREMENT OF A BASE LINE.
ORDNANCE SURVEY. DETERMINATION OF THE
LENGTH OF A DEGREE. FIGURE AND SIZE OF THE
EARTH. MEASUREMENT OF THE MOON'S DISTANCE.
567. WE now come to the measurement of the actual
distances. We have already said that astronomers use as
a basis for their investigations the methods employed
by land surveyors, and these methods are based on the
measurement of angles. As was stated in Art. 515, when
we have two angles and one side of any triangle given,
we can by means of trigonometry find out all about the
triangle, whether we have at one of its angles a tower we
cannot reach, or the Sun, or a star. This problem gene-
rally resolves itself into measuring with great accuracy
a base line, and then taking at either end of it the angle
between the other end and the object. For this purpose
it is necessary, however, that the base line shall be of
some appreciable length with reference to the distance of
the object, or shall subtend a certain angle at the object
itself ; for it is clear that if at the object the line is so
T
274 ASTRONOMY.
small that it is reduced to a mere point, the lines joining
the two ends of it and the object will be parallel.
In Fig. 52., if the lengths of the base lines Bffff' be
known, and the base lines subtend a measureable angle
at a, and the other angles are also known, the distance
from a to either c, d, e, f, g, or ^, in the triangle represented
is easily determined. Now if a be supposed to represent a
distant tower which a land surveyor cannot reach, but the
distance of which he is anxious to determine, he will
measure his base line on a level field, and observe the
angles. Similarly, if a be supposed to represent the
Moon, Mars, or Venus, under the same conditions, it is
clear that if cd, ef, or gh, represent two places on the
Earth some thousand miles apart, the distance between
which is accurately known, exactly the same process as
that employed by the land surveyor in the former case will
enable the astronomer to determine the distance of the
Moon, Mars, or Venus, because the. Moon is always, and
the planets named sometimes, sufficiently near to operate
upon in this manner. This is called determining the
Moon's or a planet's parallax.
568. If the parallax is very small, our instruments fail
us ; we cannot make the instruments large enough and
perfect enough to measure the exact angle. This happens
in the case of the Sun — that body is too far off to permit
of this mode of measuring its distance.
569. There is this difference, however, between the
cases : in the former the land surveyor could find the
distance of the tower, if he did not know the size of the
Earth ; but in the latter the size of the Earth must be
known to begin with, as it is impossible to measure directly
the distance of places far apart ; and their real distance
can only be calculated from a knowledge of their relative
positions on a globe the size of which is accurately
known.
DETERMINATION OF DISTANCES. 275
Before, therefore, astronomers could determine the dis-
tance of the nearest celestial body, the Moon, to say
nothing of the more distant ones, it was necessary that
the size of the Earth should be accurately known.
570. This has been accomplished by means of surveys,
or triangulations, of different parts of the Earth's surface —
that of England for instance. Here for a moment we
come back to the work of ordinary surveyors. In the
first instance, a base line was measured on one of the
smoothest spots that could be found. One of those chosen
was on the sandy shore on the east side of Lough Foyle,
in Ireland : the length of this line was measured with
most consummate care by means of bars of metal, the
length of which, at a given temperature, was exactly
known, and which was, at the time of observation, cor-
rected for expansion or contraction due to variations of
temperature. The bars were not placed close together,
and the intervals between them were measured by means
of microscopes. The base line by these means was
measured to within a small fraction of an inch.
571. At the station at each end of this base line was
placed a theodolite, or azimuth instrument (Art. 521), for
determining the horizontal angles between the other station
and the prominent objects visible, such as hill-tops or
church-towers, &c.: by such means, referring back to
Fig. 52, and representing the base line on Lough Foyle
by cd, ef, or gh^ and any prominent object by a, the dis-
tance from both stations was determined ; in other words,
the dimensions of each triangle were determined. Each
station, the position of which with reference to the base
line was thus established, was made in turn the centre of
similar observations, until the length and breadth of the
United Kingdom had been covered with a network of
triangulation. In each triangle, as the work advanced,
the new sides, so to speak, were determined from the
T 2
276 ASTRONOMY.
length of the side previously calculated from the obser-
vations which had gone before, the dimensions of the sides
first calculated depending upon the base line actually
measured.
572. When all the triangulations were complete, it was
possible to show on a large sheet of paper the exact posi-
tions of all the stations chosen for the triangulation, and to
measure the exact distances between them. The accuracy
of the work was verified at the end by calculating the
side of a certain triangle on Salisbury Plain, and then
testing the accuracy of the calculated length of the side
(which depended upon the accuracy of the one previously
determined, and so on, till at last it depended upon the
accuracy of the base line actually measured in Ireland,)
by actually measuring the side itself. The agreement
between the two determinations was nearly perfect.
The map of the United Kingdom has been constructed
by determining the positions of the principal stations in
this way, and then filling in the triangles by a similar
process on a smaller scale.
573. Now, how do we connect the map of England
with the size of the Earth ? In this way : it enables us to
measure the length of a degree of latitude.
574. What this means will have already been gathered
from what was said in Art. 159. As the Earth is round
(or round enough for our explanation), if it were possible to
walk along a meridian from the equator to either pole, the
stars in our zenith would change ; we should begin with
a star of o° declination over our head, and we should finish
with a star of 90° declination over our head, having passed
over 90° of latitude ; and if it were possible to measure
exactly how far we had walked, we should have the
measure of a quarter of the Earth's circumference.
575- But this is impossible ; what can be done is to
measure the change in zenith distance of the same star, or
DETERMINA TION OF DISTANCES. 277
the zenith distances of two stars the positions of which are
accurately known, in countries which have been accurately
triangulated and mapped. For instance, we can make
such observations at the Observatories of Greenwich and
Edinburgh, which are nearly on the same meridian, and
determine the difference of the zenith distance of the
same star observed at both. Now, thanks to the Ord-
nance Survey, the distance between the two Observatories
is known to within a few inches, so we at once have the
following proportion : —
Difference of zenith \ . ( Difference of \ . . 0 . / Length of a
distance ) ' I distance J ' ' I degree.
and then if the Earth were round,
i° : 360° : : length of i° : circumference of the Earth.
576. That the Earth is not quite round has been de-
monstrated by such surveys as the one we have referred to,
made near the equator, and in higher northern latitudes
than England. It has been found that the length of a
degree in different latitudes varies as follows : —
Mean Lat. Length of i° in
o English feet.
India 12 362,956
» l6 363,044
France 45 364,572
England 52 364,951
Russia 56 365,291
Sweden 66 . .» . . . . .,,365,744
It follows from these measurements, that near the
equator we have to go a shorter distance to get a change
of zenith distance of i° than near the poles ; consequently
the Earth's surface is more curved at the equator and
more flattened at the poles than it is in middle latitudes.
278 ASTRONOMY.
577. From these varying lengths of a degree we can
determine not only the amount of polar compression of
the Earth, but its circumference, and therefore its dia-
meters, which are as follow : —
English feet.
Equatorial diameter .... 41,848,380
Polar „ .... 41,708,710
But this is not all. The most recent results of the
various triangulations have taught us that the Earth is
not quite truly represented by an orange— at all events,
unless the orange be slightly squeezed ; for the equatorial
circumference is not a perfect circle, but an ellipse, the
longer and shorter equatorial diameters being respectively
41,852,864 and 41,843,896 feet. That is to say, the
equatorial diameter which pierces the Earth from long.
14° 23' East to 194° 23' east of Greenwich is two miles
longer than that at right angles to it*
578. Having now the exact form and dimensions of the
Earth, it is easy for us to determine the distance between
any two places the positions of which on the Earth's
surface are accurately known.
579. We are, therefore, in a position to measure the
distance of the Moon, if we find that, as seen from two
places as far apart as possible, say Greenwich and the Cape
of Good Hope, there is a sensible change in the position
she apparently occupies on the background of the sky ;
for the line joining the two places may be used as a base
line, and observations may be made on the Moon at each
end of it, that is, at the two stations named, exactly as
observations were made at each end of the base line at
Lough Foyle.
580. As the two stations are not visible from each other,
what is done in each case is to measure the polar distance
* Mem. Roy. Ast. Soc. vol. xxix. 1860.
DETERMINA TION OF DISTANCES. 279
of the Moon (north polar distance at Greenwich and
south polar distance at the Cape), and it is clear that,
in the case of a star, N. P. D. + S. P. D. would be equal
to 1 80°.
I P
Fig. 58. — Measurement of the Moon's distance.
This premised, in Fig. 58, on which a section of the Earth
is shown, let E represent the centre of the Earth, G the
observatory at Greenwich, and C that at the Cape of
Good Hope, both situated nearly on the same meridian.
As the stars are so distant that they appear in the same
position viewed from all parts of the Earth — because, as
seen from them, the diameter of the Earth is reduced to
a point — the dotted parallel lines, SG and S'C represent
the apparent position of a star, S, as seen from Greenwich
and the Cape. For the same reason the dotted lines,
GP and CP1, parallel to the axis of the Earth, represent
the apparent position of the north and south poles of
the heavens as seen from the places named. The angle
PGS therefore represents the north polar distance of the
star as seen from Greenwich ; the angle P CS' represents
280 ASTRONOMY.
the south polar distance of the same star observed
at the Cape : and these two angles will of course make
up 1 80°.
It is seen from the diagram that the north polar
distance of the Moon as seen from Greenwich, which is
observed, is greater than that of the star.
Similarly, the south polar distance as seen from the
Cape, which is also observed, is greater than that of the star.
Therefore these two polar distances added together are
greater than 180°, greater in fact by the angles SGM
and SCM, which are equal to GME + CME = GMC.
The angle GMC is determined by observation to be
about i J° : if, therefore, we know the length of the base
line joining Greenwich, in addition to the two angles
observed and the one deduced, plane trigonometry enables
us easily to determine the lines MG, MC, and ME, which
are the distances of the Moon from Greenwich, the Cape,
and the centre of the Earth respectively.
581. It also enables us to determine the angles GME
and CME, which represent the parallax: (Art. 543) of the
Moon as observed at Greenwich and the Cape respectively.
In this manner the mean equatorial horizontal parallax
of the Moon has been determined to be nearly 57' 6".
LESSON XLVI. — DETERMINATION OF THE DISTANCES
OF VENUS AND MARS : OF THE SUN. TRANSIT OF
VENUS. THE TRANSIT OF 1882.
582. This method may be adopted to determine the
distance of Venus when in conjunction with the Sun, and
of Mars when in opposition ; but it is only applicable in
the former case when Venus is exactly between us and
DETERMINA TION OF DISTANCES. 28 [
the Sun, or when she is said to transit or pass over his
disc — when, in short, we have a transit
of Venus ; of which more hereafter.
583. In the case of Mars in op-
position, there is, however, another
method by which his distance may be
determined by observations made at
one observatory. In this method the
base line is not dispensed with, but
instead of using two different places
on the Earth's -surface, and deter-
mining the actual distance between
them, we use observations made at
the same place at an interval of twelve
hours ; in which time, of course, if we
suppose them to be made on the
equator, the same place would be at
the two extremities of the same dia-
meter, that is 8,000 miles apart : if
the observations are not made actually
on the equator, it is still easy, knowing
exactly the shape and size of the
Earth, to calculate the actual differ-
ence. Fig. 59, which represents a
section of the Earth at the equator,
will explain this method. O and O'
represent the positions of the same
observer at an interval of twelve hours,
the Earth being in that time carried
half round by its movement of rota-
tion ; M the planet Mars ; and *.9 a ,
star of the same declination as the
planet, the direction of the star being
the same from all points of the surface
as from the centre. At O, when Mars is rising at the place
282 ASTRONOMY.
of observation, let the observer measure the distance the
planet will appear to the east of the star ; at (7, when
Mars is setting at the place of observation, and therefore
when the Earth's rotation has carried him to the other
end of the same diameter, let him again measure the
distance the planet will appear to the west of the star.
He will thus determine, as in the case of the Moon, the
angle the line joining the two places of observation sub-
tends at the planet. In the case of observations made at
the equator, the Earth's equatorial diameter forms the base
line. The angle it subtends is determined by observa-
tion; and this can be accomplished, although both the
Earth and Mars are moving in the interval between the
two observations, as the motion of both can be taken into
account. Here again then, when the size of the Earth
is known, the distance of Mars can be determined by
plane trigonometry.
584. As seen from the Sun, the Earth's diameter is so
small that it is useless as a base line, and consequently
the Sun's distance cannot be thus measured.
585. The Sun's distance can however be obtained
directly by a method pointed out by Dr. Halley in 1716,
based upon the discovery of Kepler, that the distances of
the orbits of the planets from the Sun and from each
other are so linked together, that if we could determine
any one of the distances, all the rest would follow. This
method depends upon observations of the transit of Venus.
586. As we have seen, Mars does not come so near to
us as Venus; consequently Venus is the best planet to
attack by the base-line method : but it happens that when
Venus comes nearest to us, it comes between us and the
Sun, and consequently its dark side is towards us, and we
can only see it when it happens to be exactly between us
and the Sun, when it passes over the Sun's disc as a
dark spot, a phenomenon called a transit of Venus. Un-
DETERMINATION OF DISTANCES. 283
fortunately these transits happen but rarely : the last hap-
pened in 1769; the next available one will be in 1882. On
the other hand, when they do happen, as the planet is
projected on the Sun, the Sun serves the purpose of a
micrometer, and observations may be made with the most
rigorous exactness. The measure of the Sun's distance —
one of the noblest problems in astronomy, on which
depends " every measure in astronomy beyond the Moon,
the distance of and dimensions of the Sun and every
planet and satellite, and the distances of those stars whose
parallaxes are approximately known," — is accomplished
then in this manner.
Fig. 60. — A Transit of Venus.
587. We have seen that when Venus crosses the Sun's
disc during its transit it appears as a round black spot.
Let us suppose two observers placed at two different
stations on the Earth, properly chosen for observations of
the phenomenon; one at a station^ in the northern hemi-
sphere, another at a station B in the southern one. When
Venus is exactly between the Sun and the Earth, the ob-
server at A will see her projected on the Sun, moving on
the line CD in Fig. 60 ; the southern observer at B will,
284 ASTRONOMY.
from his lower station, see the planet V projected higher
on the disc, moving on the line EF. Now, what we
require to know, in order to determine the Sun's distance,
is the distance between the lines.
If the distance between the two stations is sufficiently
great, the planet will not appear to enter on the Sun's
disc at the same absolute moment at the two stations,
and therefore the paths traversed, or the " chords," will
be different. Speaking generally, the chords will be of
unequal length, so that the time of transit at one station
will be different from the time of transit at the other.
This difference will enable us to determine the difference
in the length of the chords described by the planet, and
consequently their respective positions on the solar disc,
and the amount of their separation. Now, this separation
is what we want to know.
588. We already know the relative distances of Venus
from the Earth and Sun ; they are. as 28 to 72 nearly ;
and whatever the absolute distances may be, the value of
the separation of the two chords, in miles, will be the
same. It is evident, for instance, that if the Sun were
exactly as far from Venus on one side as we are on the
other, and the observers occupied the two poles of the
Earth, the separation would be equal to the Earth's dia-
meter ; but as the Sun is further from Venus than we are,
in the proportion of 72 to 28, if the transit were observed
from the two poles, the separation of the two chords on
the Sun would amount to 18,000 miles ; and this proportion
holds good whatever the distance.
589. If it were possible to photograph the Sun at the
same moment at the two stations, the thing would be
done ; we could at once measure the amount of separation,
determinate its proportion to the whole diameter of the
Sun, and determine the size of the Sun, whence its dis-
tance would at once follow, as we could at once determine
DETERMINA TION OF DISTANCES. 285
how great an angle the Earth's semi-diameter would sub-
tend at that same distance, which, in fact, would be the
Sun's parallax (Art. 542).
59O. Simultaneous observations, however, are out of
the question; so the observations take this form. The
moments of ingress and egress are carefully noted at both
stations,, and the differences between the two chords will
show us on what part of the Sun they lie ; this known, it
is easy to determine the separation.
Fig. 61. Fig. 62.
As the difference between the observed times of transit
at the two stations is the quantity which determines
the amount of separation, it is important to make this
difference as great as possible, as then any error bears a
smaller proportion to the observed amount.
591. This is accomplished by carefully choosing the
stations, bearing the Earth's rotation well in mind. Let
us introduce this consideration, and see, not only how
it modifies the result, but also with what anxious foresight
astronomers prepare for such phenomena, and why it was
requisite in 1769, and will be again necessary in 1882, to
go so far from home to observe them.
Let us take the transit of 1882. We already know the
instant and place (true perhaps to a second of time and
286
ASTRONOMY.
arc) at which the planet will enter and leave the solar
disc ; in other words, we know exactly how the Earth will
be hanging in space as seen from the Sun — how much the
south pole will be tipped up— how the axis will exactly
lie — how the Earth will be situated at the moments of
'Sabring Lan<f
Fig- 63.— Illuminated side of the Earth at Ingress, Dec. 6d. 2h.
ingress and egress. Fig. 61 will show how the planet will
appear to cross the Sun as seen from the Earth. Fig. 62
shows the same circle with lines reversed, representing
the points of ingress and egress, as viewed in the same
direction as the illuminated side of the Earth is viewed.
DETERMINA TION OF DISTANCES. 287
592. Now if we suppose two planes cutting the centre
of the Earth and those parts of the Sun's limb at which
the planet will enter and leave the solar disc, we shall see
in a moment that some parts of the Earth will see the
planet enter the disc sooner than others. Some parts, on
Snbnna La n
Fig, 64.— Illuminated side of the Earth at Egress, Dec, 6d. 8h.
the other hand, will see it leave the disc later : in other
words, according to the position of a place with reference
to the plane of which we have spoken, both the ingress
of the planet and its egress will appear to take place
earlier or later, as the case may be.
288 ASTRONOMY.
Now, if we can find a place where both the ingress
will be accelerated and the egress retarded, and another
where the ingress is retarded and the egress is accelerated^
we shall get what we want, the greatest difference in the
duration of the transit, — the greatest difference i-n the
length of the chords, of which we have before spoken.
Selecting, then, the parts of the Earth at which the
duration of transit would be shortest, it has been found
that on the seaboard of the United States of America
the ingress is retarded by a quantity represented by 0-95,
(the maximum being 2*00), and the egress is accelerateci
by a quantity which, in the mean, is 0*83 nearly ; so that
the whole shortening is represented by 178. That locality,
therefore, is very favourable.
Selecting,, secondly, the parts of the Earth at which the
duration of transit would be longest, it has been found
that the choice is more limited, and the practical diffi-
culties rather greater.
It will be necessary to make one set of observa-
tions at some station on the Antarctic Continent. It has
further been found that the place must be in yh east
longitude nearly. Such a position can be found between
Sabrina Land and Repulse Bay. Here the whole lengthen-
ing of transit would be represented by i'6i — a very large
amount (the maximum being 2*00). Combining this with
the observations at Bermuda, the whole difference of dura-
tion would be represented by 3 '41 (the maximum being
4*00). This point near Sabrina Land is, in fact, the only
one which is suitable for the observation.
DETERMINA TION OF DISTANCES. 298
LESSON XLVI I.— COMPARISON OF THE OLD AND
NEW VALUES OF THE SUN'S DISTANCE. DISTANCE
OF THE STARS. DETERMINATION OF REAL SIZES.
«
593. The value of the Sun's distance obtained from the
observations of the last transit was about 95,000,000 miles-
The value of the distance recently determined by other
means is about 91,000,000.
H
The old value of the parallax obtained by Bessel
from the transit of Venus was 8-578
The newvalue obtained by Hansen, from the Moon's
parallactic equation . 8*916
„ „ Winnecke, from the ob-
servations of Mars . 8*964
» » Stone 8*930
„ „ Foucault, from the velo-
city of light .... 8*960
„ „ Leverrier, from the mo-
tions of Mars, Venus,
and the Moon . . . 8*950
The difference between the old and new values, = two-
fifths of a second of arc, amounts to no more than a
correction to an observed angle represented by the appa-
rent breadth of a human hair viewed at the distance of
about 125 feet.
594. Having now obtained the Sun's distance, we can
advance another step in our investigations : — I. We
began with a measured base line in a field, and by it
U
290 ASTRONOMY.
determined the distance of a tower we could not reach.
II. Then the Earth was measured, and, with a base line
between Greenwich and the Cape of Good Hope, the
distance of the Moon was determined. III. Next, using
the Earth's diameter (8,000 miles) as a base line, the dis-
tance of Mars was determined, then that of the Sun itself.
IV. Having thus obtained the distance of the Sun, we are
in possession of a base line of enormous dimensions, for
it is clear that the positions successively occupied by
our Earth in two opposite points of its orbit will be
182,000,000 miles apart. Here then are we really sup-
plied with a base line sufficient to measure the distances
of the stars ? No ; in the great majority of cases the
parallax is so small that there is no apparent difference
in the position as observed in January or July, February
and August, &c. As seen from the fixed stars, that
tremendous line is a point ! Now an instrument such as
is ordinarily used should show us a parallax of one second
—that is, an angle of i" formed at the star by half the
base line we are using — and a parallax of i" means that
the object is 206,265 times further away than we are from
the Sun, as the Sun's distance is the half of our new base
line. Here then we get a limit. If the star's parallax
is less than i", the stars must be further away than
9 1, 000,000 miles multiplied by 206,265 '
595. In the great majority of cases, however, the true
zenith-distance of a star is the same all the year round ;
and as this true place results from the several corrections
referred to in the last chapter being applied, when there
is a slight variation, it is very difficult to ascribe it to
parallax, as a slight error in the refraction, or the presence
of proper motion in the star, would give rise to a greater
difference in the places than the one due to parallax, as
in no case does this exceed i". Hence, as long as the
problem was attacked in this manner, very little progress
DETERMINA TION OF DISTANCES. 291
was made, the parallax of a Centauri alone being obtained
by Henderson = c/'-QiS/.
Bessel, however, employed a method by which the
various corrections were done away with, or nearly so.
He chose a star having a decided proper motion, and
compared its position, night after night, by means of the
micrometer only, with other small stars lying near it which
had no proper motion, and which therefore he assumed to
be very much further away, and he found that the star
with the proper motion did really change its position
with regard to the more remote ones, as it was observed
from different parts of the Earth's orbit. This method
has since been pursued with great success : here is a
Table showing some of the results :—
Star.
Parallax.
Distance.
Sun's distance
=;- I.
a Centauri .
0-9187
224,OOO
61 Cygni ....
0-5638
366,000
1830 Groombridge
0*226
912,000
70 Ophiuchi . . .
0-16
1,286,000
a Lyrae ....
0-155
i,337,ooo
Sirius
O'lS
I 375 ooo
Arcturus ....
j
0*127
1,624,000
Polaris ....
0*067
3,078,000
Capella ....
0-046
4,484,000
596. So much for the measurement of distances. When
the distance of a body is known, and also its angular
measurement, its size is determined by a simple propor-
tion, for the distance is, in fact, the radius of the circle on
which the angle is measured.
U 2
292 ASTRONOMY.
There are 1,296,000 seconds in an entire circum-
1296000
ference : there are therefore - —7- seconds in that part
3
1296000
of a circumference equal to the diameter, and ^
2
= 206265" in that part of the circumference equal to the
radius.
We have then
c distance ) .. ( the angular ) ( •'
in miles 1 \ in miles ]" \ diameter f ( 206265;
or, calling the real diameter d9 and the distance D,
D X angular diameter
d 206265
597. For instance, the mean angular diameter of the
Moon is 3i'8"-8 = i868"'8, and its distance is 237,640
miles. To determine its real diameter, we have
237640 X i868"'8
d" 206265 = 2153 miles.
In Table II. of the Appendix are given the greatest
and least apparent angular diameters of the planets as
seen from the Earth. The reader should, from these
values and the distances given in Art. 377, determine the
real diameters for himself.
598. Knowing the real and also the apparent angular
diameter, we can at once determine the distance by trans-
posing equation I, as follows :—
= 206265 X d
angular diameter '
in seconds
CHAPTER IX.
UNIVERSAL GRAVITATION.
LESSON XLVIIL— REST AND MOTION. PARALLELO-
GRAM OF FORCES. LAW OF FALLING BODIES. CUR-
VILINEAR MOTION. NEWTON'S DISCOVERY. FALL
OF THE MOON TO THE EARTH. KEPLER'S LAWS.
599. IF a body at rest receive an impulse in any direc-
tion, it will move in that direction, and with a uniform
motion, if it be not stopped. If on the Earth we so set a
body in motion — a cricket-ball, for instance, along a field —
it will in time be impeded by the grass. If we fire a cannon-
ball in the air, the cannon-ball will in time be arrested by
the resistance of the air ; and, moreover, while its speed
is slackening from this cause, it will fall, like everything
else, to the Earth, and its path will be a curved line. If
it were possible to fire a cannon in space where there is
no air to resist, and if there were no body which would
draw it to itself, as the Earth does, the projectile would
for ever pursue a straight path, with an uniform rate of
motion.
600. In fact, the moment a stone is thrown from the
hand, or a projectile leaves the cannon, on the Earth,
there is superadded to the original velocity of
294 ASTRONOMY.
projection an acceleration directed towards the
Earth ; and the path actually described is what is called
a resultant of these two velocities.
6O1. Let us make this clear with regard to motion in a
straight line on the Earth's surface. Suppose that the
cricket-ball A, in Fig. 65, receives an impulse which will
send it to B in a certain time ; it will move in the direction
AB. Suppose, again, it receives an impulse that will send
A
Fig. 65. — Parallelogram of Forces.
it to C in the same time ; it will move in the direction A C,
and more slowly, as it has a less distance to go. But
suppose, again, that both these impulses are given at the
same moment ; it will neither go to B nor to C, but will
move in a direction between those points. The exact
direction, and the distance it will go, are determined by
completing the parallelogram A BCD, and drawing the
diagonal AD, which represents the direction and amount
of the compound motion.
6O2. All bodies on the Earth fall to the Earth, as an
apple from a tree, and it is from this tendency that the
idea of weight is derived, and of the difference between
a light body and a heavy one. This idea, however, is often
incorrectly held, because the atmosphere plays such a
large part in every-day life. For instance, if we drop a
shilling and a feather, the feather will require more time
to fall than the shilling : and it would at first appear that
the tendency to fall, or the gravity, of the feather was
different from that of the shilling. This, however, is not
so ; for if we place both in a long tube exhausted of air,
UNIVERSAL GRAVITATION. 295
we shall find that both will fall in the same time : and it
is usual to measure gravity or attraction by the space
through which bodies fall, in feet and inches, in one second
of time. The difference in the time of fall in air, then, de-
pends upon the unequal resistance of the air to the bodies.
6O3. Various machines have been invented at different
times for measuring exactly the rate at which a body falls
to the Earth, and it has been found that the rate of fall
goes on increasing with the distance fallen through. Thus
a body falls in one second through a distance of 16^ feet,
and has then acquired a velocity of 32 \ feet per second,
and so on: so that, generally, the space fallen through in
any given number of seconds is equal to 16^ feet multi-
plied by the square of the time. If we represent the
space fallen through by S, the velocity acquired after a
fall of one second by G, and the time by /, we have
604. Now if a cannon-ball were left unsupported at
the mouth of the gun, it would fall to the Earth in a
certain time : when fired from the gun it has superadded
to its tendency to fall a motion which carries it to the
target, but in its flight its gravity is always at work, and
the law referred to in Art. 60 1, holds good in this case
also, which is one of curvilinear motion : and as the
cannon-ball is pulled out of its straight course towards
the target by the action of the Earth upon it, pulling it
down, so in all cases of curvilinear motion there is a
something deflecting the moving body from the rectilinear
course.
605. Sir Isaac Newton was the first to see that the
Moon's curved path was similar to the curved path of a
projectile, and that both were due to the same 'cause as
the fall of an apple, namely, the attraction of the Earth.
296 ASTRONOMY.
He saw that on the Earth's surface the tendency of
bodies to fall was universal, and that the Earth acted, as
it were, like a magnet, drawing everything free to move
to it, even on the highest mountains ; why not then at
the distance of the Moon ? And he immediately applied
the knowledge derived from observation on falling bodies
on the Earth to test the accuracy of his idea.
606. Newton's discovery of the law of gravitation
teaches us that the force of gravity is common to all kinds
of matter. Its law of action may be stated thus: — The
force with which two material particles attract
each other is directly proportional to the pro-
duct of their masses, and inversely proportional
to the square of the distances between their
centres. Now the intensity of a force is measured by
the momentum, or joint product of velocity and mass,
produced in one second in a body subjected to this force,
and this measure of force must be" remembered in dis-
cussing the above law of gravity.
607. Thus, if our unit of mass be one pound, and if
this pound be allowed to fall towards the Earth, at the end
of one second it will be moving with the velocity of 32 J
feet per second. Now let the mass be a ten-pound weight ;
it might be thought that, since the Earth attracts each
pound of this weight, and therefore attracts the whole
weight with ten times the force (see above definition)
with which it attracts one pound, we should have a much
greater velocity produced in one second. The old school-
men thought so, but Galileo showed that a ten-pound
weight will fall to the ground with the same velocity as a
one-pound weight. A little consideration will show us
that this is quite consistent with our definition of gravity
and our definition of force. Undoubtedly the ten-pound
weight is attracted with ten times the force, but then there
is ten times the mass to move, so that even although the
UNIVERSAL GRAVITATION. 297
velocity produced in one second is no greater than in the
one-pound weight, yet if we multiply this velocity by the
mass the momentum produced is ten times as great.
608. Now, since it is each individual atom of the Earth
that attracts each individual atom of the weight, we might
expect, from our definition of gravity as well as from the
well-known law that every action has a reaction, that the
Earth, when the weight is dropped, at the end of one
second rises upwards to the weight with the same mo-
mentum that the weight moves downwards to the Earth.
No doubt it does ; but as the Earth is a very large mass,
this momentum represents a velocity infinitesimally small.
609. Again, were the Earth twice as large as it is, it
would produce in one second of time a double velocity,
or 64 \ feet per second ; and were it only half as large, we
should have only half the velocity, or 163^ feet per second
produced.
610. Hence we see that at the surface of the Moon
the gravity is very small, whereas at the surface of the
Sun it is enormous. There remains to consider the
element of distance.
A body at the surface of the Earth, or 4,000 miles from
its centre, acquires, as we have seen, by virtue of the
Earth's attraction, the velocity of 32^ feet per second at
the end of one second. During this one second it has
not, however, fallen 32^- feet; for, as it started with no
velocity at all, and only acquired the velocity of 32^- feet
at the end, it will have gone through the first second with
the mean velocity of 16^5- feet; it will, in fact, have fallen
16^5- feet from rest in one second. Now this body, at the
distance of the Moon, or sixty times as far off, would
only fall in one second towards the Earth a distance of
fo * ^Q or ~r~ of a foot. Let us look into this a
little closer.
298
ASTRONOMY.
611. Experiment shows, as we have seen, that attrac-
tion, or gravity, at the Earth's surface causes a body to
fall 16^ feet in the first second of fall, after which it has
acquired a velocity of 2X 16^=32^ feet during the second
second, and so on, according to the square of the time
(Art. 603). Thus
feet.
Fall in i second = i X i6^§- =
„ 2 seconds = 4 X 16^- =
» 3 „ = 9 X 16^ =
feet.
257A
402^.
Fig. 66. — Action of Gravity on the Moon's path.
612. The Moon's curved path is an exact representation
of what the path of our cannon-ball (Art. 604) would be at
the Moon's distance from the Earth; in fact, the Moon's
path MM' , in Fig. 66, is compounded of an original im-
pulse in the direction at right angles to EM, and therefore
in the direction MB, and a constant pull towards the Earth
— the amount of pull being represented for any arc by the
line MA (Fig. 66). To find the value of MA, let us take
the arc described by the Moon in one minute, the length
of which is found by the following proportion :—
27 d. yh. 43m. : im. : : 360° : 33" nearly = MM'.
UNIVERSAL GRAVITATION. 299
From this value of the arc, the length of the line MA is
found to be 16^ feet when ME = 240,000 miles. That
is, a body at the Moon's distance falls as far in one minute
as it would do on the Earth's surface in one second — that
is, it falls a distance 60 times less. A body on the Earth's
surface is 4,000 miles from the Earth's centre, whereas the
Moon lies at a distance of 240,000 from that centre — that
is, exactly (or exactly enough for our present purpose)
60 times more distant.
613. It is found, therefore, that the deflection pro-
duced in the Moon's orbit from the tangent to its path in
one second is precisely of ^|^ a foot. Here we see that,
as the Moon is sixty times further from the Earth's centre
than a stone at the Earth's surface, it is attracted to the
Earth 60 X 60, or 3600 times less. In fact, the force is
seen experimentally to vary inversely as the square of the
distance of the falling body from the surface. It was
this calculation that revealed to Newton the law of
universal gravitation.
614. Long before Newton's discovery, Kepler, from
observations of the planets merely, had detected certain
laws of their motion, which bear his name. They are as
follows : —
I. Each planet describes round the Sun an orbit 01
elliptic form, and the centre of the Sun occupies
one of the foci.
II. The areas described by the radius- vector of a
planet are proportional to the time taken in de-
scribing them.
III. If the squares of the times of revolution of the
planets round the Sun be divided by the cubes of
their mean distances, the quotient will be the same
for all the planets.
300 ASTRONOMY.
615. We have already in many places referred to the
first law : II. and III. require special explanation, which
we will give in this place. We stated in Art. 293 that the
planets moved faster as they approached the Sun; 1 1. tells
how much faster. The radius-vector of a planet is the
line joining the planet and the Sun. If the planet were
always at the same distance from the Sun, the radius-
vector would not vary in length; but in elliptic orbits
its length varies; and the shorter it becomes, the more
rapidly does the planet progress. This law gives the
exact measure of the increase or decrease of the rapidity.
Fig. 67. — Explanation of Kepler's second law.
616. In Fig. 67 are given the orbit of a planet and
the Sun situated in one of the foci, the ellipticity of the
planet's orbit being exaggerated to make the explanation
clearer. The areas of the three shaded portions are equal
to each other. It is readily seen that where the radius-
vector is longest, the path of the planet intercepted is
shortest, and vice 'versa. This, of course, is necessary to
UNIVERSAL GRAVITATION.
301
produce the equal areas. In the figure, the arcs P P^
P2 P3, and P± P5J are those described at mean distances,
perihelion and aphelion respectively, in equal times ; there-
fore, as a greater distance has to be got over at perihelion
and a less one at aphelion than when the planet is situated
at its mean distance, the motion in the former case must
be more rapid, and in the latter case slower, than in other
parts of the orbit.
617. The third law shows that the periodic time of a
planet and its distance from the Sun are in some way
bound together, so that if we represent the Earth's dis-
tance and periodic time by i, we can at once determine
the distance of, say, Jupiter from the Sun, by a simple
proportion ; thus —
Square of
Earth's
period
I X I
Square of
Jupiter's
period
ir86xi r86
Cube or
Jupiter's
distance
That is, whatever the distance of the Earth from the Sun
may be, the distance of Jupiter is 1/140 times greater.
618. The following table shows the truth of the law
we are considering : —
Mean distance.
lime squarea.
Periodic Time.
Earth = i.
Distance cubed.
Mercury .
87-97 •
. 0-3871 .
- 133,421
Venus
. 22770 .
. 0-7233 .
• I334I3
Earth
• 365^5 •
. i -oooo ,
• 133,408
Mars . .
. 686-98 .
. 1^237 .
• 133,410
Jupiter
• 4332'58 •
. 5-2028 .
• 133,294
Saturn
. I0759'22
. 9-5388 .
- 133,401
Uranus .
. 30686-82 .
. 19*1824 .
. 133,422
Neptune .
. 60126-71
. 30-0368 .
• 133,405
302 ASTRONOMY.
LESSON XLIX. — KEPLER'S SECOND LAW PROVED.
CENTRIFUGAL TENDENCY. CENTRIPETAL FORCE.
KEPLER'S THIRD LAW PROVED. THE CONIC
SECTIONS. MOVEMENT IN AN ELLIPSE.
619. As these laws were given to the world by Kepler,
they simply represented facts ; for, owing to the backward
state of the mechanical and mathematical sciences in his
time, he was unable to see their hidden meaning. This
was reserved for the genius of Sir Isaac Newton, after
Kepler's time.
5<
Fig. 68. — Proof of Kepler's second law.
62O. Newton showed that all these laws established the
truth of the law of gravitation, and flowed naturally from
it. In Fig. 68, let 6" represent the centre of the Sun, and
P a planet, at a given moment. During a very short time
this planet will describe a part of its orbit PP ', and its
radius-vector will have swept over the area PSP'. If no
new force intervene, in another similar interval the planet
will have reached />", the area P'SP" being equal to
PSP1 according to Kepler's second law. But the planet will
really describe the arc FB, and the area FSB will be
equal to P'SP" \ as the triangles are equal, and on the
same base, the line P"B will be parallel to P'S; and
completing the parallelogram P' P" BC, we see that the
UNIVERSAL GRAVITATION. 303
planet at Pf was acted upon by two forces, measured by
P'P" and P'C — that is, by its initial velocity and a force
directed to the Sun. Hence Kepler's second law shows
that this force is directed towards the Sun.
621. A good idea of the tendency of bodies to keep
in the direction of their original motion may be gained
by attaching a small bucket, nearly rilled with water,
to a rope, and by swinging it round gently ; the ten-
dency of the water to fly off will prevent its falling out
of the bucket ; and it will be found that the more rapidly
the bucket is whirled round, the greater will be this
tendency, and therefore the tighter will be the rope.
622. The circular movement of the bucket is repre-
sented in Fig. 69. A represents the bucket, OA the rope ;
let us suppose that the bucket receives an impulse which,
A £
Fig. 69. — Circular Motion.
in the absence of the rope, would have sent it in the direc^
tion A B with an uniform motion. In a very short time,
being held by the rope, it will arrive at c, and Ad
measures the force applied by the rope. Call this force f,
we have AD = 4//2 (i).
304 ASTRONOMY.
Further, the distance traversed — that is, Ac— is deter-
mined by the velocity (y) of the bucket, and the time
taken (t\ so we have Ac = vt; and the arc Ac being
taken equal to its chord, we have, representing the radius
by R,
Ac = 2A X AD (2).
But A c = vt, and A D = \ft* ; therefore,
y/2 = 2R X i//2 (3).
i/2
and/ = - (4).
This gives the acceleration in feet independently of the
mass m of the bucket ; if the force is sought in pounds, m
must be introduced, and the equation becomes
This measures, in the instance we have quoted, the amount
of pull on the rope, the rope holding the bucket by a force
ui i/2
- equal in amount and opposite. The first is called
R
the centrifugal tendency; the second the centripetal
force.
As the entire circumference 2 TT R (where TT = 3-1416
and R = radius) is traversed at the velocity v in the time /,
we have
271-7? = I//,
that is, v = - ...... (6).
Substituting this in equation 4, we get
R
or - 2 T . . . . (7).
UNIVERSAL GRAVITATION. 305
623. Now if for a moment the orbits of the planets be
treated as circles, this formula gives the acceleration of
their motion — that is, the force of attraction on a unit of
mass at the planet's distance, as attraction does exactly
for the planet what the rope does for the bucket.
Let it next be supposed that several planets at
different distances from the Sun represented by R R'R"
.... are revolving round him in different times, T T' T"
.... we shall have in each case
R R' R"
_.
But, by Kepler's third law, in each case the squares of the
times of revolution T2 T'2 T"2 are equal to the cubes of
the distance from the Sun R* R's, &c. Calling this law
Z, we have in each case
L — -y^ L
Dividing the former equations by these, we get
that is, in each case/J or the attraction on the unit of mass,
varies in the inverse ratio of the square of the distances.
624. Newton also showed, in a similar manner, that
the attraction is proportional to the product of the masses
of the bodies ; and that if we take two bodies, the Sun
and our Earth, for instance, we may imagine all the gravi-
tating energies of each to be concentrated at their centres,
and that if the smaller one receives an impulse neither
exactly towards nor from the larger one, it will describe an
orbit round the larger one, the orbit being one of the conic
sections — that is, either a circle, ellipse, hyperbola, or
parabola. Which of these it will be depends in each case
upon the direction and force of the original impulse, which,
X
ASTRONOMY.
as the movements of the heavenly bodies are not arrested
as bodies in movement on the Earth's surface are, is
still at work, and suffices for their present movements.
Were the attraction of the central body to cease, the
revolving body, obeying its original impulse, would leave
its orbit, in consequence of the centrifugal tendency it
acquired at its original start : were the centrifugal tendency
to cease, the centripetal force would be uncontrolled, and
the body would fall upon the attracting mass.
Fig. 70.— The Conic Sections : A B the circle ; C D the ellipse ; E F the
hyperbola ; G H the parabola.
625. Next let us inquire how it is that equal areas are
swept over in equal times. This is easily understood in a
circle, and may be explained as follows in the ellipse :—
In a circle the motion is always at a right angle to the line
joining the two bodies ; this condition of things occurs only
UNIVERSAL GRAVITATION. 307
at two points in an ellipse, i.e. at the apses, or extremities
of the major axis — the aphelion and perihelion points.
626. In Fig. 71 the planet P is moving in the direction
PT,ihe tangent to the ellipse at the place it occupies, and
this direction is far from being at right angles to the Sun,
so that the attractive force of the Sun helps the planet
along. At Pr it is equally evident that the attractive force
Fig. 71.— Diagram showing how the varying velocities of a body revolving
in an orbit are caused and controlled.
is pulling the planet back. At P" the attractive force is
strong, but the planet is enabled to overcome it by the
increased velocity it has acquired from being acted upon
at P ; while at P'" the attractive force is weak, but the
planet is not able to overcome it, on account of its velocity
having been enfeebled from being acted upon as at P*.
LESSON L.— ATTRACTING AND ATTRACTED BODIES
CONSIDERED SEPARATELY. CENTRE OF GRAVITY.
DETERMINATION OF THE WEIGHT OF THE EARTH ;
OF THE SUN ; OF THE SATELLITES.
627. As every particle of matter attracts every other
particle, the smaller bodies attract the larger ones ; so
that, to speak of the Sun and Earth as examples, the Earth
attracts the Sun as well as the Sun the Earth.
X 2
308 ASTRONOMY.
628. Now, it must here be remarked that, at the same
distance, the attraction of one body on another is quite
independent of the mass of the attracted body. If we
take the Earth as the attracting body, for instance, and
the Sun and Jupiter when equally distant from the Earth
as the attracted bodies, leaving for the present mutual
attractions out of the question, the Earth's attractive
power over both is equal, and is the same as it would
be on a pea or on a mass larger even than the Sun at the
same distance. That is, if we had the Sun, Jupiter, a
pea, and a mass larger than the Sun, at the same distance
from the Earth, the Earth's attraction would pull them
through the same number of feet and inches in one
second of time.
629. Secondly, still dealing with attracted bodies at
the same distance from the attracting body, not only
will the attraction be the same for all, but it will depend
upon, and vary with, the mass of the attracting body.
630. Thirdly, if the attracted bodies be at different
distances, the power of the attracting body over them
varies inversely as the square of its distances from them.
631. If we consider the mutual attractions, then the
attraction of a body with, say, one unit of mass will be
1,000 times less than that of a body with 1,000 units of
mass— this proportion being, of course, kept up at all
distances. If in the case of two bodies, such as the Earth
and Sun, all the attraction were contained, say, in the
Sun, then the Earth would revolve round the Sun, the
Sun's centre being the centre of motion ; but as the Earth
pulls the Sun, as well as the Sun the Earth, a conse-
quence of this is, that both Earth and Sun revolve round
a point in a line joining the two, called the centre of gravity.
The centre of gravity would be found if we could join the
two bodies by a bar, and find out the point of the bar by
which they could be suspended, scale fashion. It is clear
UNIVERSAL GRAVITATION. 309
that if the two bodies were of the same mass, such a
point of suspension would be half-way between the two ;
if one be heavier than the other, the point of suspension
will approach the heavier body in the ratio of its greater
weight. In the case of the Sun and Earth, for instance,
the centre of gravity of the two lies within the Sun's
surface.
Fig. 72. — Centre of Gravity and Motion in the" case of equal masses.
A and £, two equal masses ; c, the centre of gravity and motion.
632. It follows from what has been stated, that the
masses of the Sun, and of those planets which have satel-
lites, can be determined, if the mass of our own Earth
and the various distances of the attracted bodies from
their centres of motion are known : for, knowing the
mass of our Earth, we can compare all attracting bodies
with it, as their attractions are independent of the masses
Fig- 73- — Centre of Gravity and Motion in the case of unequal masses.
A and £, two unequal masses ; c, the centre of gravity and motion.
of the attracted bodies (Art. 628), and the law that attrac-
tion varies inversely as the square of the distance is
established (Art. 606) ; so that we can exactly weigh them
against the Earth. Thus we can weigh the Sun, because
the planets revolve round him ; and from the curvature of
their paths we can determine his pull, and contrast it with
the Earth's pull. We can similarly weigh Jupiter, Saturn,
ASTRONOMY.
Uranus, Neptune, and the double stars whose distances
are known.
Fig. 74. — Showing the differences in the curvature of the orbits of Jupiter
and the Earth. J K and EF, the fall towards the Sun.
633. Further, attraction is not only a controlling force
keeping each planet and satellite in its orbit with regard
to the central body, but it is a disturbing or perturbating
force, seeing that every body attracts every other body:
hence its effects are of the most complicated kind, as
will be seen presently. By carefully watching the per-
turbating effects of our Moon on the Earth ; and of those
planets which have no satellites, and of the satellites of
Jupiter, Saturn, Uranus, and Neptune upon each other;
their masses, in terms of the Earth's mass, have also
been determined. Let us see how this has been done.
UNIVERSAL GRAVITATION. 311
634. The mass of a body means its weight. It is
not sufficient, therefore, to determine the Earth's bulk or
volume, because it might be light, like a gas, or heavy, like
lead. The mean density, or specific gravity, of its mate-
rials— that is, how much the materials weigh, bulk for
bulk, compared with some well-known substance such as
water— must be determined.
635. The following methods have been used to deter-
mine the density of the Earth : —
I. By comparing the attractive force of a large ball
of metal with that of the Earth.
II. By determining the degree by which a large moun-
tain will deflect, or pull out of the upright towards
it, a plumb-line.
III. By determining the rate of vibration of the same
pendulum —
(a) on the top and at the bottom of a mountain.
(b) at the bottom of a mine, and at the Earth's
surface.
636. It will be sufficient here to describe the first-
mentioned method, which was adopted by Cavendish in
1798, and called the Cavendish experiment. The weight
of anything is a measure of the Earth's attraction. Caven-
dish, therefore, took two small leaden balls of known
weight, and fixed them at the two ends of a slender
wooden rod six feet long, the rod being suspended by a
fine wire. When the rod was perfectly at rest, he brought
two large leaden balls, one on either side of the small
ones. If the large balls exerted any appreciable attrac-
tive influence on the smaller ones, the wire would twist,
allowing each small ball to approach the large one near
it ; and a telescope was arranged to mark the deviation.
637. Cavendish found there was a deviation. This
enabled him to calculate how large it would have been
312 ASTRONOMY.
had each large ball been as large as the Earth. He then
had the attraction of the Earth, measured by the weight
of the small balls, and the attraction of a mass of lead as
large as the Earth, as the result of his experiment. The
density of the Earth then was to the density of lead as
the attraction of the Earth to the attractive force of a
leaden ball as large as the Earth. This proportion gave
a density for the Earth of 5*45 as compared with water,
the density of lead being 11-35 compared with water.
Fig- 75- — The Cavendish Experiment. AB, the small leaden balls on the
rod C. DE, the suspending wire. FG, the large leaden balls on one side
of the small ones. HKy the large leaden balls in a position on the other
side.
With this density, the weight or mass of the whole
Earth can readily be determined; it amounts in round
numbers to
6,<XK3,c)Co,oc>o,<XK3,ooo?ooo,c>oo tons :
but this number is not needed in Astronomy ; the relative
masses indicated in Art. 147 are sufficient.
638. Then as to the mass of the Sun. The question
is, how many times is the mass of the Sun greater than
UNIVERSAL GRAVITATION. 313
the mass of the Earth ? We shall evidently get an answer
if we can compare the action of the Earth and Sun upon
the same body. Now, on the Earth's surface, i.e. at 4,000
miles from its centre, a body falls 16^ feet in a second.
Can we determine how far it would fall at 4,000 miles
from the centre of the Sun? This is easy, as in the
case of the Moon (Art. 612) we can determine how far
the Earth falls to the Sun in a second : this is found
to be '0099 feet. But this is at a distance of 91,000,000
miles from the Sun's centre. We must bring this to
4,000 miles from the Sun's centre, or 22,750 times nearer.
Now as attraction varies inversely as the square of the
distance, we must multiply the square of 22,750 by '0099
to represent the fall of the body in one second at 4,000
miles from the Sun's surface. The result is 5,123,758
feet. Then
ft. ft.
: 5,123,758 :: i : 318,641.
The mass of the Sun therefore is roughly 318,641 times
greater than that of the Earth. The correct mass is
stated in Table IV. of the Appendix.
639. Similarly from the orbit of any one of the satel-
lites we determine its rate of fall at 4,000 miles from
the centre of any of the planets, and then compare it
with the 1 6 ^ feet fall on the Earth's surface.
640. Or we may determine the Sun's mass from
equation 7 (Art. 622) in this way : —
The centrifugal tendency of the Earth in her orbit
= 4-7T2 ^ ; and this equally measures the Sun's attrac-
tion, which is proportional to his mass, and inversely as
the square of the distance ; so that we have
Sun's mass R
~
3 H ASTRONOMY.
R*
Or Sun's mass = 47r2 ^ (2)-
f
Again, we may take 47? 2 -^ to represent the Earth's
attraction on the Moon ; so that
rz
Earth's mass = 4^ . . . . (3).
Dividing the Sun's mass by the Earth's mass (that is,
dividing equation i by equation 3), we get —
Sun's mass ft3 t^
Earth's mass =" ~T3 X r3 * * * ' ^'
We next substitute values :—
ft = the Sun's distance) ^ ., ,.
c i_ T- i_ ( = 11,571 Earth diameters,
from the Earth )
T = the Earth's year . . = 365-265 days.
r = the Earth's distance) 0 _ , ,.
r v TV/T ( — 29*982 Earth diameters,
from the Moon )
/ = the Moon's period . = 27*321 days.
So equation 4, becomes :
Sun's mass II57I3 x 27-3212
Earth's mass 365*2653 X 29'9823
This should be worked out.
In the same way we may determine the mass of Jupiter,
Saturn, Uranus, or Neptune.
64-1. The force of gravity on the surface of the Sun or
a planet, compared to that on our Earth, may be deter-
mined in the following manner : —
Let us take the case of the Sun. If we take the Earth's
radius, mass, and gravity, each as i, then the gravity on
the Sun's surface compared to that on the Earth's will
be =
Sun's mass 314760
Square of distance io7'<
= 27.
UNIVERSAL GRAVITATION. 315
LESSON LI. — GENERAL EFFECT OF ATTRACTION.
PRECESSION OF THE EQUINOXES : HOW CAUSED.
NUTATION. MOTIONS OF THE EARTH'S Axis. THE
TIDES. SEMI-DIURNAL, SPRING, AND NEAP TIDES.
CAUSE OF THE TIDES. THEIR PROBABLE EFFECT
ON THE EARTH'S ROTATION.
642. What has gone before will show that it is the
attraction of gravitation which causes the planets and
satellites to pursue their paths round the central body ;
that their motion is similar to that of a projectile fired on
the Earth's surface, if we leave out of consideration the
resistance of the air ; and that Newton's law enables us
to determine the masses of the Sun and of the other
bodies from their motions, when the mass of the Earth
itself is known.
64-3. Moreover, the orbit which each body would de-
scribe round the Sun or round its primary, if itself and
the Sun or primary were the only bodies in the system,
is liable to variations in consequence of the existence of
the other planets and satellites, as these attract the body
as the Sun or primary attracts it, the attractions varying
according to the constantly changing distances between
the bodies. These irregular attractions, so to speak, are
called perturbations, and the resulting changes in the
motions of the bodies are called inequalities if the
disturbances are large, and secular inequalities if they
are of such a nature that they extend over a long period
of time.
644. These perturbations, and their results on the orbits
of the various bodies, are among the most difficult sub-
jects in the whole domain of astronomy, and a sufficient
316 ASTRONOMY.
statement and explanation of them would carry us beyond
the limits of this little book. We will conclude this
chapter, therefore, with a reference to two additional
effects of attraction of a somewhat different kind, and of
the utmost importance, on the Earth itself. One results
from the attractions of the Sun and Moon on the equa-
torial protuberance, and is called the precession of tlie
equinoxes; the other is due to the attractions of the Sun
and Moon on the water on the Earth's surface, whence
result the tides.
645. Let the equatorial protuberance of the Earth be
represented by a ring, supported by two points at the
extremities of a diameter, and inclined to its support as
the Earth's equator is inclined to the ecliptic. Let a long
string be attached to the highest portion of the ring, and
let the string be pulled horizontally, at right angles to the
two points of suspension, and away from the centre of the
ring. This pull will represent the Sun's attraction on the
protuberance. The effect on the ring will be that it will
at once take up a horizontal position ; the highest part of
the ring will fall as if it were pulled from below, the
lowest part will rise as if pulled from above.
646. The Sun's attraction on the equatorial protuber-
ance in certain parts of the orbit is exactly similar to the
action of the string on the ring, but the problem is compli-
cated by the two motions of the Earth. In the first place
— in virtue of the yearly motion round the Sun — the pro-
tuberance is presented to the Sun differently at different
times, so that twice a year (at the solstices) the action is
greatest, and twice a year (at the equinoxes) the action
is nil; and, in the second place, the Earth's rotation is
constantly varying that part of the equator subjected to
the attraction.
647. If the Earth were at rest, the equatorial pro-
tuberance would soon settle down into the plane of the
UNIVERSAL GRAVITATION. 317
ecliptic ; in consequence, however, of its two motions,
this result is prevented, and the attraction of the Sun on
a particle situated in it is limited to causing that particle
to meet the plane of the ecliptic earlier than it otherwise
would do if the Sun had not this special action on the
protuberance. If we take the presentation of the Earth
to the Sun at the winter solstice (Fig. 10), and bear in
mind that the Earth's rotation is from left to right in the
diagram, it will be clear, that while the particle is mount-
ing the equator, the Sun's attraction is pulling it down ;
so that the path of the particle is really less steep than the
equator is represented in the diagram : towards the east
the particle descends from this less height more rapidly
than it would otherwise do, as the Sun's attraction is
still exercised : the final compound result therefore is, that
it meets the plane of the ecliptic sooner than it otherwise
would have done. .
64-8. What happens with one particle in the protu-
berance happens with all ; one half of it, therefore, tends
to fall, the other half tends to rise, and the whole Earth
meets the strain by rolling on its axis : the inclination of
the protuberance to the plane of the ecliptic is not altered,
but, in consequence of the rolling motion, the places in
which it crosses that plane precede those at which the
equator would cross it were the Earth a perfect sphere :
hence the term precession.
649. In what has gone before, the sphere inclosed in
the equatorial protuberance has been neglected, as the
action of the Sun on the spherical portion is constant : it
plays an important part, however, in averaging the pre-
cessional motion of the entire planet during the year,
acting as a break at the solstices, when the Sun's action
on the equatorial protuberance is. most powerful, and
continuing the motion at the equinoxes, when, as before
stated, the Sun's action is nil.
ASTRONOMY.
65O. Also, for the sake of greater clearness, we have
omitted to consider the Moon, although our satellite
plays the greatest part in precession, for the following
reason : The action referred to does not depend upon
the actual attractions of the Sun and Moon upon the
Earth as a whole, which are in the proportion of 120
to i, but upon the difference of the attraction of each
upon the various portions of the Earth. As the Sun's
Fig. 76. — Showing the effects of Precession on the position of the
Earth's axis.
distance is so great compared with the diameter of the
Earth, the differential effect of the Sun's action is small ;
but, as the Moon is so near, the differential effect is so
considerable that her precessional action is three times
that of the Sun.
651. An important result of the motion of the pro-
tuberance has now to be considered. The change in the
UNIVERSAL GRAVITATION.
319
position of the equator, which follows from the rolling
motion, is necessarily connected with a change in the
Earth's axis.
652. In Fig. 76, let ab represent the plane of the ecliptic,
CQ a line perpendicular to it, hfe the position of the
equator at any time at which it intersects the plane of the
equator in e. The position of the Earth's axis is in the
direction Cp. When, by virtue of the precessional move-
ments, the equator has taken up the position Ikg, crossing
the plane of the ecliptic in g, the Earth's axis will occupy
the position Cpr.
653. The lines Cp and Cp' have both the same inclina-
tion to CQ. It follows, therefore, that the motion of the
Earth's axis due to precession consists in a slow revolution
round the axis of the celestial sphere, perpendicular to the
plane of the ecliptic.
654. Superadded to the general effect of the Sun and
Moon in causing the precession of the equinoxes, or luni-
solar precession, is an additional one due to the Moon
alone, termed nutation.
Fig- 77-— Explanation of Nutation.
655. The Moon's nodes perform a complete revolution
in nineteen years (Art. 244) ; consequently for half this
period the Moon's orbit is inclined to the ecliptic in the
same way as the Earth's equator is, though in a less
degree (mn, Fig. 77, ^representing the mean inclination).
During the other half the orbit is inclined so that its
320
ASTRONOMY.
divergence from the plane of the Earth's equator is the
greatest possible (pg)*
656. It follows, from what we have already seen in the
case of the Sun, that in the former position the preces-
sional effect will be small, while in the latter position it
will be the greatest possible.
657. Hence the circular movement of the axis which
causes the precession of the equinoxes is not the only
one ; there is another due to the nutation. Were the
pole at rest, we should have from this latter cause a small
ellipse described every nineteen years ; but as it is in
motion, as we have seen in Art. 653, the two motions are
compounded, so that the motion of the pole of the equator
round the pole of the ecliptic, instead of being circular, is
waved.
Fig: 78. — Apparent motion of the Pole of the Equator, P, round the Pole of
the heavens (or Ecliptic), n.
658. The effect of these motions of the Earth's axis
on the apparent position of the heavenly bodies, and the
corrections which are thereby rendered necessary, have
already been referred to at length in Lesson XLIII.
We next come to the tides.
659. The waters of the ocean rise and fall at intervals
of 12 hours and 25 minutes — that is, they rise and fall
twice in a lunar day (Art. 423). When the tide is
highest, we have high water, or flood ; after this the tide
ebbs, or goes down, till we have low' water, or ebb ; and
UNIVERSAL GRAVITATION. 321
after this the water flows, or increases again to the next
high water, and so on.
66O. We not only have two tides in a lunar day, but
twice in the lunar month — about three days after new and
full Moon, the tides are higher than usual : these are
the spring tides. Twice also, three days after the Moon
is in her quadratures, they are lower than usual : these are
the neap tides. It will be gathered from the foregoing
that the tides have something to do with the Moon ; in
fact, these phenomena are due to the attraction of the
Sun and Moon on the fluid envelope of the Earth, and,
as in the case of luni-solar precession, not only is it to the
differential action of these bodies, and not to their abso-
lute action, that the effect is due, but the two periods
correspond with the lunar day and the lunar month,
because the Moon's differential attraction is far greater
than that of the Sun.
€61. If we take the Sun's distance as 23,142 terrestrial
radii, and its mass as 314,760 times that of the Earth, the
Earth's action on a particle of water at its surface being
represented by I, then - — py^ anc* ^ — ~~2 vyi^ represent
the Sun's attraction on a particle on the sides of the
Earth adjacent to it and turned away from it respectively.
*oi 23
In the case of the Moon we shall have, similarly, -
'0123
and ~7~^ ; it is readily seen that the differential attrac-
tion, therefore, in the case of the Moon is much greater
than in the case of the Sun.
662. It may be stated, generally, that the semi-diurnal
tides are caused by the Moon (although there is really a
smaller daily tide caused by the Sun), that the semi-
monthly variation in their amount is due to the Sun's
tide being add^d to that of the Moon when she is new and
Y
322 ASTRONOMY.
full — that is, when the Sun and Moon are pulling together ;
and subtracted from it when at the first and last quarters
they are pulling crosswise, or at right angles to each
other.
663. The double daily tide arises from the action of
the Moon on both the water and the Earth itself. On the
side under the Moon the water is pulled from the
Earth, piled up under the Moon, as the Moon's action on
the surface-water is greater than its action on the Earth's
centre ; but, for the same reason, the Moon's attraction on
the Earth's centre is greater than its attraction on the water
on the opposite side of the Earth, so that in this case, as
the solid earth must move with its centre, the Earth is
pulled from the water. There are, therefore, always
two tides on the Earth's surface ; and it is to the motion or
undulation of the Earth under this double tide — which is
a state of the water merely without progressive motion —
nearly at rest under the Moon, and under which state the
Earth (as it were) slips round— that the occurrence of two
tides a day instead of one is due. There is, in fact, an
ellipsoid of water inclosing the Earth, which always
remains with its longer axis pointing to the Moon.
664-. The existence of a state of high water under, or
nearly under, the Moon, does not depend merely upon the
direct attraction of our satellite upon the particles imme-
diately underneath it, but upon its action upon all the
particles of water on the side of the Earth turned to it,
all of which tend to close up under the Moon. The force
acting upon these particles is called the tangential com-
ponent of the attraction ; and this is by far the most
powerful cause of the tides, as it acts at right angles to
the Earth's gravity, whereas the direct attraction of the
Moon acts in opposition to it.
665- The spring and neap tides, which, as we have
seen, depend upon the combined or opposed action of the
UNIVERSAL GRAVITATION. 323
Sun and Moon in longitude, are also influenced by the
difference of latitude between the two bodies. Of course,
that spring tide will be highest which occurs when the
Moon is nearest her node, or in the ecliptic. The apex of
the semi-diurnal tide also follows the Moon throughout
her various declinations.
666. The phenomena of the tides are greatly compli-
cated by the irregular distribution of land. The time of
high water at any one place occurs at the same period
from the Moon's passage over the meridian ; this period
is different for different places. The interval at new or
full Moon between the times of the Moon's meridian
passage and high water is termed the establisLment of
the port.
667. Although in the open ocean the velocity of the
tidal undulation may be 500 or even 900 miles an hour,
in shallow waters the undulation is retarded to even
seven miles ; at the same time its height is increased. The
average height of the tide round the islands in the Atlantic
and Pacific Oceans is but 3^ feet ; whereas at the head of
the Bay of Fundy it is 70 feet. As the tidal undulation
does not move so rapidly as the Earth does, as it is regu-
lated by the Moon, it appears to move westward while the
Earth is moving eastward ; and it has been suggested that
this apparent backward movement acts as a break on the
Earth's rotation, and that, owing to the effects of tidal
action, the diurnal rotation is, and has been, constantly
decreasing in velocity to an extremely minute extent. At
all events, if the sidereal day be assumed to be invariable,
it is impossible to represent the Moon's true place at
intervals 2,000 years apart by the theory of gravitation.
On this assumption the Moon, looked upon as a time-
piece, is too fast by 6" or I2s. (nearly) at the end of each
century. This may be due to the fact that our standard
Y 2
324 ASTRONOMY.
of measurement of the sidereal day is too slow; and it has
been calculated that this part of the apparent acceleration
of the Moon's mean motion maybe accounted for by sup-
posing that the sidereal day is shortening, in consequence
of tidal action, at the rate of ^th part of a second in
2,500 years.
APPENDIX.
TABLE I. Astronomical Symbols and Abbreviations.
II. Elements of the Planets.
III. „ Satellites.
IV. „ Sun.
V. „ Moon.
VI. Time.
VII. Conversion of Intervals of Sidereal Time into Mean Time.
VIII. Mean Time into Sidereal Time,
APPENDIX.
TABLE I.
EXPLANATION OP' ASTRONOMICAL SYMBOLS
AND ABBREVIATIONS.
Signs of the Zodiac.
0
0.
r Aries . .
0
VI.
±± Libra . . . .
1 80
I.
8 Taurus
• 30
VII.
>n Scorpio . .
210
II.
n Gemini
. 60
VIII.
t Sagittarius .
240
III.
25 Cancer . .
. 90
IX.
vf Capricornus
270
IV.
ft Leo . . .
. 120
X.
ss Aquarius
300
V.
TYJJ Virgo . . '
. ISO
XI.
x Pisces . .
330
The Sun.
The Moon.
0
£
Major Planets.
$ Mercury
\
y
Jupiter.
? Venus.
\
Saturn.
0 or 6 The Earth.
¥
Uranus.
<J Mars.
¥
Neptune.
A Comet.
A Star.
4 Conjunction.
D Quadrature.
5 Opposition.
6 Ascending Node.
8 Descending Node.
# Sextile.
h Hours.
m Minutes of Time.
s Seconds of Time.
0 Degrees.
' Minutes of Arc.
" Seconds of Arc.
R.A. or yR. or a., Right
Ascension.
Dec1- or D. or 5., Declina-
tion.
N. P. D., North Polar
Distance.
328
APPENDIX.
Minor Planets.
0 Ceres.
© Circe.
© Asia.
0 Pallas.
© Leucothea.
@ Leto.
0 Juno.
@ Atalanta.
© Hesperia.
© Vesta.
© Fides.
@ Panopea.
0 Astraea.
(33) Leda.
© Niobe.
0 Hebe.
© Lsetitia.
@ Feronia.
0 Iris.
© Harmonia.
© Clytie.
0 Flora.
© Daphne.
© Galatea.
0 Metis.
© Isis.
© Eurydice.
© Hygeia.
© Ariadne.
@ Freia.
,0 Parthenope.
© Nysa.
© Friga.
0 Victoria.
© Eugenia.
@ Diana.
0 Egeria.
@ Hestia.
© Eurynomc.
@ Irene.
© Aglaia.
© Sappho.
@ JEunomia.
@ Doris.
© Terpsichore,
@ Psyche.
© Pales.
© Alcmene.
@ Thetis.
© Virginia.
© Beatrix.
@ Melpomene.
© Nemausa
© Clio.
@ Fortuna.
@ Europa.
© Io.
@ Massilia.
© Calypso.
@ Semele.
0 Lutetia.
(54) Alexandra.
© Sylvia.
0 Calliope.
(55) Pandora
@ Thisbe.
@ Thalia.
© Melete.
© Julia.
0 Themis.
© Mnemosyne.
©
@ Phocea.
(g) Concordia.
© yEgina.
0 Proserpine.
@ Olympia.
©
(g) Euterpe.
@ Echo.
©
@ Bellona.
@ Danae.
©
0 Amphitrite.
(g) Erato.
@ Arethusa.
0 Urania.
(g) Ausonia.
@ y^gle.
Q Euphrosyne.
(g) Angelina.
@ Clotho.
@ Pomona.
Q Maximiliana.
g) lanthe.
(g) Polyhymnia.
@ Maia.
APPENDIX.
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APPENDIX. 33'
TABLE IV.— THE SUN.
Old Value. New Value.
Equatorial horizontal parallax . . 8"'5776 8"'94O
Mean distance from th£ Earth . 95,274,000 91,430,000
{Variable with the latitude. The ro-
tation in 24 hours of mean solar
time is expressed by the formula,
865'±i65'j/>; 1 1.
Diameter in miles 888,646 852,584
Inclination of axis to prlane of ecliptic 82° 45'} * ~Q
Longitude of Node 73 40 )
Mass ^j C 354,936 3H,76o
Density . . . . j 0-250
Volume ....-} Sl 1,415,225 1,245,126
Force of gravity at I
Equator . . . j 287 27-2
Apparent diameter as seen from the Earth-
Maximum . 32*36" 41
Minimum . 31 32-0
TABLE V.
ADDITIONAL ELEMENTS OF THE MOON.
Mean Horizontal Parallax .... = 57' 2"7o
Mean Angular Telescopic Semi-diameter 15 33*36
Ascending Node of Orbit 13° 53' 17"
Mean Synodic Period 29*530588715 days
Time of Rotation 27-321661418 „
Inclination of Axis to the Ecliptic . . i° 30' io'f<8
Longitude of Pole ?
Daily Geocentric Motion ..... J3 LTO 35
332 APPENDIX.
Mean Revolution of Nodes .... 6793d<39io8
„ „ Apogee or Apsides 3232'57343
Density, Earth as I = 0*56654
Volume, „ = 0*02012
Force of Gravity at Surface, Earth as I = J
Bodies fall in One Second 2'6 feet
TABLE VI.— TIME.
I. — THE YEAR.
Mean Solar Days,
d. h. m. s.
The Mean Sidereal Year . . . 365 6 9 9-6
The Mean Solar or Tropical Year 365 5 48 46*054440
The Mean Anomalistic Year. . 365 6 13 49-3
II. — THE MONTH.
Lunar or Synodic Month . . . 29 12 44 2-84
TropicaLMonth ...... 27 7 43 471
Sidereal „ 27 7 43 11-54
Anomalistic,, 27 13 18 37-40
Nodical „ 27 5 5 35 60
III.— THE DAY.
The Apparent Solar Day, or interval
between two transits of the Sun
over the meridian variable.
The Mean Solar Day, or interval be-
tween two transits of the Mean Sun
over the meridian 24 o o
(Astronomers reckon this day from noon to noon, through the 24 hours. )
The Sidereal Day 23 56 4*09
The Mean Lunar Day ....... 24 54 o
APPENDIX
TABLE VII.
333
For converting Intervals of SIDEREAL Time into Equivalent Intervals
of MEAN SOLAR Time.
HOURS.
MINUTES.
SECONDS.
FRACTIONS OF
A SECOND.
V
I
V
E
g
|
"" V
H
Equivalents
H
Equivalents
h
Equivalents
jj£
1
in
Mean Time.
"rt
V
8
in
Mean Time.
*73
V
in
MeanTime.
"13
8
"« C
11
IS
"2
"2
«^CH
c/5
c/3
c/5
c/3
W
h
h. m s.
m
m. s.
s.
s.
s.
s.
i
0 59 50*17°
I
3
o 59-8362
2 59 5085
i
3
0-9973
2-9918
Ooi
0*04
0-0099
0-0399
2
i 59 40*340
5
4 59 1809
5
4-9864
0-07
0-0698
3
4
2 59 3o'5"
3 59 20 "68 1
7
9
10
6 58-8532
8 58-5256
9 58 3617
7
9
10
69809
89754
99727
0*10
0-13
O IU
0-0597
o 1296
o 1596
5
4 59 10-852
ii
10 58 1979
12 57 8703
ii
13
io"97oo
12-9645
O'IQ
O'22
0-1895
02194
6
5 59 i'022
15
14 57-5426
15
I4'959i
0-25
0-2493
7
6 58 5i*i93
17
19
l6 5? -2T^O
18 56-8873
17
169536
18-9481
028
o 30
02792
0-2591
8
7 58 41-363
20
J9 56 7235
20
'9 '9454
o 31
0-3092
9
8 58 3i*534
21
23
20 56 5597
22 56 2320
21
23
209427
22-9372
034
o'37
03690
10
9 58 21-704
25
24 55-9044
25
249318
0*40
o 3989
ii
10 58 11-874
27
29
26 55^767
28 55-2490
27
29
26*9263
28-9208
o'43
0-46
0-4288
04587
12
ii 58 2-045
3°
29 55 0852
30
29-9181
o"49
0-4887
13
12 57 52*215
33
30 54 9214
32 54 '5937
31
33
30-9154
329099
0-52
04986
0-5186
14
13 57 42-3^6
35
34 54 2661
35
34-9045
o'55
0*5485
15
T4 57 32-556
37
39
36 53-9384
38 53-6108
37
39
36-8590
0-58
o'6i
05784
0-6083
16
15 57 22-727
40
39 53 '4 470
40
39 8908
0*64
06382
17
T^i CT TO'Rrw
41
40 53-283!
41
40-8881
o 67
o C682
*
iu 57 J ^ °y/
43
42 52-9555
43
4* '8826
0*70
06981
18
17 57 3-067
45
44 52-6278
45
44-8772
°'73
0-7280
19
1 8 56 53-238
47
49
46 52-3002
48 51-9725
47
49
46-8717
48-8662
0-76
0-79
o'7579
0-7878
20
19 56 43-409
50
49 51-8087
50
49-8635
o 82
o 8178
21
20 56 33-579
53
50 51-6449
52 51-3172
53
508608
52-8553
0-85
088
0-8477
0*8776
22
21 56 23-749
55
54 50-9896
55
54'8499
o 90
0-8975
23
22 56 13-920
57
59
56 50 '6619
58 50-3343
57
59
56-8444
58 8389
o 91
094
09075
09374
«4
«3 56 4'oc;o
60
59 50-1704
60
59-8362
°"97
0-9673
334
APPENDIX,
TABLE VIII.
For converting Intervals of MEAN SOLAK Time into Equivalent
Intervals of SIDEREAL Time.
HOURS.
MINUTES
SECONDS.
FRACTIONS OF
A SECOND.
V
d
V
u
•s|
|
H
Equivalents
in
H
Equivalents
in Sidereal
H
Equivalents
in Sidereal
j
i '•"
cH
V _
9
Sidereal Time.
c
rt
Time.
c
9
Time.
%
11
6
y
t)
V
3 CJ
s
S
B
%
Is
Wc/3
h.
h. in. s.
m.
m. s.
s.
s.
s.
s
i
i o 9*856
i
3
i o 1643
3 0-4928
i
3
i "0027
3-0082
O'OI
0*04
O OIOO
0-0401
2
2 o 19-713
5
5 0-8214
5
5 '0137
o 07
0*0702
3
3 o 29-569
7
9
7 i 1499
9 * '4785
7
9
7-0192
9 "0246
O'lO
0-13
0-1003
0-1303
4
4 o 39 '425
10
10 1-6428
10
10 "0274
o'i6
0-1604
: 5
5 o 49 282
ii
J3
Hi "8070
13 2-1356
ii •
13
IT 'O3OI
1 3 '0356
0*19
0 22
0-1905
0"2206
1 6
6 o 59-138
15
15 2-4641
15
1 5 04"
0-25
0-2507
7
7 i 8-995
17
19
17 2-7927
19 3'I2I2
i?
19
170465
19*0520
0-28
O'3O
0-28o8
0-3008
8
8 i 18-851
20
20 3-2855
20
20-0548
0-3I
0-3108
9
9 i 28-708
21
23
21 3-4498
23 3'7783
21
23
21 '0575
23-0630
0'34
0-37
0-3409
0-3710
10
jo i 38 564
25
25 4-1069
25
25^85
0*40
o'4on
ii
ii i 48 421
27
29
27 4"4354
29 4 '764o
27
29
27-0739
29-0794
043
0-46
0-4312
04613
12
12 i 58-277
30
30 4-9282
30
3O-O82I
049
o-49r3
13
13 2 8-134
31
33
31 5'0925
33 5-42"
31
33
3I '0849
33-0904
0-50
0-52
0-5014
05214
14
14 2 17-990
35
35 5 -7496
35
35'0958
o"55
o-55i5
15
15 2 27-847
37
39
37 6-0782
39 6-4067
37
39
37'IOI3
39 '1068
0-58
o'6i
o 5816
o 6167
16
16 2 37-703
40
40 6-5710
40
40-1095
0*64
06417
i?
17 2 47-560
4i
43
4i 6-7353
43 7-0638
4i
43
41-1123
43'"77
o 67
o 70
0-6718
0*7019
18
18 2 57-416
45
45 7-3924
45
45-1232
0-73
o 7320
47
47 7 '7209
47
47-1287
0-76
o 7621
J9
J9 3 7'273
49
49 8-0495
49
49'i342
0'79
0-7922
20
20 3 17-129
SC-
50 8-2137
So
50-1369
0-82
0-8222
21
21 3 26-985
SI
53
51 8-^780
53 8-7066
5i
53
51-1396
53 MS*
0-85
o 88
0-8523
0-8824
22
22 3 36*842
55
55 9'°35i
55
55 'i 5o6
0*90
0-9025
23
23 3 46-698
57
59
57 9 'o637
59 9-6922
57
59
57'i56i
59'l6i5
0-91
0*94
09125
o '9426
,24
24 3 56-555
60
6:> 9 8565
60 60-1643
o"97
09727
INDEX.
INDEX,
INCI.UDING
AN ETYMOLOGICAL VOCABULARY OF ASTRONOMICAL TERMS.
Abbreviations used in astronomy,
see Appendix, Table I.
Aberration of light (ab, from, and
errare, to wander, as the apparent
place is not the true one), 449 ; re-
sults of, 539 : how the aberration
place of a star is corrected. 540 ;
constant of, 539 ; spherical and chro-
matic, of lenses, 466.
Absorption of the atmospheres of
stars, 68 ; of sun, 119.
Acceleration, Secular, of the
moon's mean motion, an increase
in the velocity of the moon's motion
caused by a slow change in the
eccentricity of the earth's orbit, see
667.
Achromatism of lenses, 464.
Adams discovers Neptune, 277.
Adjustments of altazimuth, 523 ;
transit circle, 524 ; equatorial, 485.
Aerolite .(aV/P, the air, and Aiefor,
a stone), a meteor which falls to
the earth's surface, 314,
Areosideritf.s (
and
iron), an iron which falls to the
earth's surface, 314.
Air, refraction of the, 450-52 ; table
of refraction, 537.
Almanac, Nautical, 557.
Altazimuth (contraction ofJtttttufe
and azimuth], an instrument for
measuring altitudes and azimuths,
486; when used, 521 ; description of,
522 ; how to use. 523.
Altitude (altitudo, height), the
angular height of a celestial body
above the horizon, 329.
Angle (angufas, a corner), the in-
clination of two straight lines to
each other, 511 ; of position, 519; the
angle formed by the line joining the
components of double stars, &c. with
the direction of the diurnal motion.
It is reckoned in degrees from the
north point passing through east,
south, and west.
Angle of the vertical, the differ-
ence between astronomical and geo-
detical latitude. It is ° at the equator
and at the poles, and attains a
maximum of n' 30" in lat. 45°.
Annular eclipses (annnlns, a ring),
see Eclipses ; annular nebulae, 85.
Anomaly (<>, not, and o/ia \ 6r, equal).
The anomaly is either true, mean, or
eccentric. The first is the true dis-
tance of a planet or comet from
perihelion ; the second what it would
have been had it moved with a mean
velocity ; and the third an auxiliary
angle introduced to facilitate the
computation of a planet's or comet's
motion.
Anomalistic year, 439.
Ansse (handles) of Saturn's ring, 271.
Aphelion (aVo, from, and rj*<o<-, the
sun), the point in an orbit furthest
from the sun, 167 ; distance of comets,
288 ; planets, 377.
Apogee faVo and in, the earth), (i)
The point in the moon's orbit furthest
from the earth, 212 ; (2) the position
in which the sun, or other body, is
furthest from the earth.
Apsis (<W/iv, a curve), plural Ap.
Sides. The line of apsides (446) is
the line joining the aphelion and
perihelion points ; it is therefore
the major axis of elliptic orbits.
338
INDEX.
Arc, Diurnal, the path described by
a celestial body between rising and
setting, 367 ; semi-diurnal, half this
path on either side of the meridian.
Arc of meridian, how measured,
Areas, Kepler's law of, 614-15.
Ari?8, First Point of, one of the points
of intersection of the celestial equator
and ecliptic, and the start-point for
RA. and celestial longitude, 328.
Ascending: node, see Node.
Ascension. Right, the angular dis-
tance of a heavenly body from the
first point of Aries, measured upon
the equator, 328.
Asteroids, a name given to the
minor planets, 280.
Atmosphere, refraction of the,
450-52 ; table of refractions, 537 ; of
sun, 119; of stars, 65; of the earth,
199, 208 ; of planets, 259, 264, 274 ;
of moon, 227.
Attraction of gravitation, see Gra-
vitation.
Axis. The axis of a heavenly body
is the line on wh*lch it rotates, 106:
the major axis of an elliptical orbit is
the line of apsides, 446 ; the minor
axis is the line at right angles to
it ; the semi-axis major is equal to
the mean distance-
Axis of the earth, its movements,
168, 547.
Axis, polar, and declination, ofequa-
torials, 484-85.
Azimuth (samatha, Arabic, to go
towards), the angular distance of a
celestial object from the north or
south point of the meridian, 329.
Base line, how measured, 570.
Belts of Jupiter, 263 ; of calms and
rains, 201-
Bissextile, 440.
Bode's law. 280.
Bolides, see Meteors, luminous.
Bond, 271.
Brilliancy, of the stars, 23 ; sun, 100 ;
moon, 218 ; minor planets, 284.
Calendar, 443.
Calms of Cancer and Capricorn, 201.
Catalogues of stars, 529.
Cavendish experiment, the, 636.
Celestial sphere, 326 et seq.\ ap-
parent movements of, 330 et seq. ; two
methods of dividing, 362 ; meridiz
329-
Centre of gravity, 631.
Centrifugal tendency, 622.
Centripetal force, 622.
Chronograph, an instrument for
determining the times of transit of a
heavenly body across the field of
view of a transit circle, or other in-
strument, with the greatest accuracy,
Circle, Declination, the circle on the
declination axis of an equatorial, by
which the declinations of celestial
bodies are measured, 485 ; great, a
circle subdividing the celestial sphere
into two equal portions ; transit, an
instrument adapted for observing the
transit of heavenly bodies across the
meridian and their zenith distance,
524 ; of perpetual apparition, a circle
of polar distance equal to the lati-
tude of the place, the stars within
which never set, 335.
Circumpolar stars, 341.
Clepsydrae, 398.
Clock, invention of, 404 ; principles
of construction, 403 ; sidereal clock,
528.
Clock-stars ; stars the positions of
which have been accurately deter-
mined, used in regulating astrono-
mical clocks and determining the
time, 558.
Cloud on Mars, 259.
Clusters of stars, 71-75.
Co-latitude of a place or a star is
the difference between its latitude
and 90°.
Collimation (cum, with, and limes,
a limit;, line of the optical axis of a
telescope; error of, the distance of
the cross wires of a telescope from
the line of collimation, 518.
Collimator, a telescope used for
determining the line of collimation in
fixed astronomical instruments, 524.
Colours of stars, 60-63.
Colures (xo\ovw, I divide), great
circles passing through the equinoxes
and solstitial colures, called the equi-
noctial and solstitial colures.
Coma (Lat. hair] of a comet, 293.
Comes (Lat. companion], the smaller
component of a double star.
Comets («ofiffrt|C, hairy) are pro-
bably masses of gas, 13, 293 ; orbits
INDEX.
339
of, 288, 297 ; distances from sun,
28'8 ; long and short period comets,
289 ; numbers recorded, 292 ; forces
at work in, 293 ; velocity of, 293 ;
are probably harmless, 294 ; division
of Biela's comet, 295 ; numbers of,
in our own system, 296.
Compression, polar, or polar flat-
tening, the amount by which the
polar diameter of a planet is less
than its equatorial one, 255.
Cone of shadow in eclipses, 242.
Conic sections, the, 624.
Conjunction. Two or more bodies
are said to be in conjunction when
they are in the same longitude or right
ascension. In inferior conjunction
the bodies are on the same side of
the sun ; in superior conjunction on
opposite sides, 378.
Constant of aberration, 539
Constellation (cnm and stella, a
star:, a group of stars supposed to
represent some figure, 35 ; classifi-
cation of, 36 ; zodiacal, 37 ; northern,
38 ; southern, 39 ; visible throughout
the year, 352 et seq. ; circumpolar,
Co-ordmates, transformation of
equatorial into ecliptic, 552.
CopernaCUS, lunar crater, 228.
Corona (LaL crown], the halo of
light which surrounds the dark body
of the moon during a total eclipse
of the sun, 246.
Corrections applied to observed
places, 536 et seq. \ for refraction,
537 ; aberration, 539 ; parallax, 543 '.
luni-solar precession and nutation,
545 et seq.
Cosmical rising and setting of a
heavenly body = rising or setting
\vith the sun.
Craters of the moon, 223 et stq.
Crust of the earth, 183 et seq. \
temperature of, 193; thickness of,
194 ; density, 195.
Culmination cnlmen,\ht top\the
passage of a heavenly body across
the meridian when it is at the highest
point of its diurnal path. Circum-
polar stars have two culminations,
upper and lower.
Curtate distance, the distance of
a celestial body from the sun or
earth projected upon the plane of
the ecliptic.
Cusp cuspis, a sharp pomt\ the
extremities of the illuminated side
of the moon or inferior planets at
the crescent phase.
Cycle of eclipses, a period after which
eclipses occur in the same order as
before, 244.
Dawes discovers Saturn's inner ring,
271.
Day, apparent and mean solar, 419 ;
sidereal and solar, 358 ;• lengths of,
in the planets, 253 ; and night, 164,
169; how caused, 171 ; how to find
the lengths of, 569.
Declination, the angular distance
of a celestial body north or south
from the equator, 328 ; circle or
parallel of, 328 ; axis of equatorial*,
485.
Degree, the 36oth part of any circle, .
574 ; length of a, how determined in
different latitudes, 576.
De I«a Rue, Mr., his lunar, solar,
and planetary photographs, 507.
Density of the earth, 195, 637 ; how
measured, 635 ; of the sun and
planets, 103, 147, 638 et seq.
Descending node, see Node.
Detonating meteors, 313.
Diameter of the earth, 153, 163 ;
moon, 211 : sun, 101 ; planets, 140;
true and apparent, 596.
Dimensions, of the sun, 101 ; earth,
153, 163; moon, an ; lunar craters,
224 ; the planets, 140 ; Saturn and
his rings, 272 ; how determined, 596.
Direct motion, see Motion.
DiSC, the visible surface of the sun,
moon, or planets.
Dispersion of light, 455 ; varies m
different substances, 465.
Distances, of stars, 25 ; how deter-
mined, 594 ; of nebulae, 90 ; of sun,
101 ; how determined, 585 et seq. ;
old and new values of, 593 ; and
planets, 139, 282 ; how determined,
582; moon, an, 212; how deter-
mined, 579 ; pclar, 329 ; how dis-
tances are measured, 567 et seq.
Double stars, see Stars.
Earth, the, is round, 150, 151 ; rota-
tion proved by Foucault, 154, 157 ;
poles, 153; equator, ib.\ diameters,
ib. : dimensions, 163 ? how deter-
Z 2
340
INDEX.
mined, 5T$etseq.; latitude and longi-
tude, 160, 161, 328 ; parallels and
meridians, 162, 328 ; tropics, circles,
and zones, 162 ; shape, 163, 196 ;
shape of orbit, 167 ; changes, 445 ;
inclination of axis, 168 ; day and
night, 164; how caused, 171; at
the po!es, 172 ; length of day and
night, 173 ; how to determine, 369 ;
seasons, iT^etseq. 447 ; structure and
past history of, 181 et seq. ; interior
temperature of, 193 ; once a star,
190 ; why an oblate spheroid, 196 ;
atmosphere, 199 et seq. 208 ; belts
of calms and rains, and trade
winds, 201 ; cause of the winds, 202 ;
elements in the earth's crust, 207 •;
in the earth's atmosphere, 208.
Apparent movements. The earth is the
centre of the visible creation, 322 ;
apparent movements of the heavens
are due to the real movements of
the, 325 ; effects of rotation, 326, 343 ;
apparent movements of the stars as
seen from different points on the
surface> 331 et seq. ; effects of the
earth's yearly motion, 344 et seq. ;
effects of attraction of, 605 ; motions
of axis, 651 et seq.
Earth-shine, 217.
Eccentricity of an crbit (ex, from,
and centrum, a centre), the distance
of a focus from the centre of an
ellipse. It is expressed by thq
ratio the distance bears to the sun's
axis major. An eccentricity of o'l,
e.g., means that the focus is one-
tenth of the sun's axis major from
the centre.
Eclipses (e»cAe<>//<9, a disappearance),
233 et seq.
Ecliptic (so called because when
either sun or moon is eclipsed it is
in this circle^, the great circle of the
heavens, along which the sun per-
forms his annual path, 363 ; plane of
the, 105, 300. The plane of the sun's
apparent, and of the earth's real,
motion, 105, 136, 300 ; obliquity of,
the angle between the plane of the
ecliptic and of the celestial equator,
Egress, the passing of one body off
the disc of another ; e g. one of the
satellites off Jupiter, or Venus or
Mercury off the sun.
Elements, chemical, present in the
sun, 123 ; fixed stars, 69 ; earth*
crust, 207 ; meteorites, 317.
Elements of an orbit are the quan-
tities the determination of which
enables us to know the form and
position of the orbit of a comet or
planet, and to predict the positions of
the body, see Appendix, Tables 1 1 .—V .,
Ellipses, 165 et seq. 624.
Elongation, the angular distance
of a planet from the sun : of Mercury
and Venus, 380.
Emersion, the reappearance of a
body after it has been eclipsed or
occulted by another ; e.g the emer-
sion of Jupiter's satellites from be-
hind Jupiter, or the emersion of a
star from behind the moon.
Enceladus, one of the satellites of
Saturn.
Envelopes of comets, 293.
Ephemeris (t?r«', for, r^pu, a day),
a statement of the positions of the
heavenly bodies for every day or
hour prepared some time before-
hand, 557.
Epoch, the time to which calcu-
lations- or positions of the heavenly
bodies are referred, 551, 555.
Equation of the centre, the differ-
ence between the true and mean
anomalies of a planet or comet ; of thq
equinoxes, the difference between
the mean and apparent equinox : of
time, the difference between true
solar and mean solar time, 415.
Equator, terrestrial, 153 ; celestial,
328.
Equatorial telescope, 4^2 ; method
of using, 535 ; horizontal parallax,
see Parallax.
Equinoxes (ceqrtns, equal, and nox,
night, ; vernal or equinoctial, the
points of intersection of the ecliptfe
and equator. When the sun occu-
pies these positions in Spring and
Autumn of the northern hemisphere,
there is equal day and night all
over the world, a small circle near
each pole excepted, 171 ; precession
of the, see Precession.
Errors, instrumental and clock, 530,
555-
Evection (etv/tere, to carry away!.
One of the lunar inequalities which
increases or diminishes her mean
longitude to the extent of i° 20'.
INDEX.
tar, 380.
Eye-pieces qf telescopes, 471 ; their
various forms, 472-73 ; transit eye-
piece, 531.
Faculse 'Lat. torcJies], the brightest
parts of the solar photosphere, 1 19.
Field of view, the portion of the
heavens visible in a telescope.
Figure of the earth, see Earth.
Fixed stars, see Stars. ,
FOCUS (Lat. heart ft <, the point at
which converging rays meet, 458.
Foci of an eclipse, 166
Foucault proves the earth's rota-
tion, 154 ; determines the velocity of
light, 450.
Fraunhofer-'s lines, 490.
Galaxy (7«XaKToc, of milk), the
Greek name for the Milky Way, or
Via Lactea.
Geocentric (-y^i, the earth, and K^V-
rpo»>, a centre), as viewed from the
centre of the earth ; latitude and
longitude, 360.
Geography, physical, 182 et seq.
Geology, 182.
Gibbous (Lat. gibbns^ bunched)
moon, 231.
Globes, use of the, 337 ; terrestrial,
159; celestial, 41; compass, 338;
brazen meridian, 338 ; wooden hori-
zon, 338 ; rectifying the globe, 339,
349 : globe, celestial, explains sun's
daily motion, 365 et seq.
Gnomon (^VW^MV, an index), a sun-
dial, 398.
Granulations on the solar surface,
JI5-
Gravitation, Universal, 606 etseq.;
the moon's path, 612 ; Kepler's laws,
614 ; results of, 642 et seq. ; pertur-
bations, 643; nutation, 654; preces-
sion, 645 ; tides, 659.
Gravity (gravis, heavy), 602 ; mea-
sure of, on the earth, 603, 61 1 ; on the
sun and planets, 641 ; centre of, 631.
Gregorian calendar, style, 443.
Gyroscope, 157.
Harvest moon, 373.
Head of comets, 291. 293.
Heavens, how to observe the, 342.
Heliacal rising or setting of a
star is when it just becomes visible
in morning or evening twilight.
Heliocentric (3 AIOT, the sun, and
Kti/Tpui/, a centre), as seen from, or
referred to, the centre of the sun ;
latitude and longitude, 360.
Heliometer (JjAmv and /itTpov, a
measure), a telescope with a divided
object-glass designed to measure
small angular distances with great
accuracy. It is so called because it
was first used to measure the sun.
Hemispheres (nut, half, and
ff<p,iiptt, a sphere), half the surface
of the celestial sphere. The sphere
is divided into hemispheres by great
circles such as the equator and
ecliptic.
Herschel, Sir W, discovers the
inner satellites of Saturn, 271 ; dis-
covers Uranus, 277.
Horizon (op*C«i I bound), true or
rational, 329; sensible, 152.
Horizontal parallax, see Parallax.
Hour angle, the angular distance
of a heavenly body from the meri-
dian.
Hour circle, the circle attached to
the equatorial telescope, by which
right ascensions are indicated, 535.
Huggins, Mr., his spectroscopic
observations, 409, 504.
Hyperbola, the, one of the conic
sections, 624.
Immersion (immergere, to plunge
into), the disappearance of one
heavenly body behind another, or
in the shadow of another.
Inclination of an orbit, the angle
between the plane of the orbit and
the plane of the ecliptic : of the
sun, 106; of the earth, 168 ; of the
axes of planets, 253.
Inequalities, Secular; perturba-
tions of the celestial bodies so small
that they only become important in a
long period of time, 643.
Inferior conjunction, see Conjunc-
tion ; planet, see Planet.
Instruments, astronomical, 518^
seq.
Irradiation, 217.
Jets in comets, 293.
JovicentriC (Jwis, of Jupiter, and
Kt-'i'Tp'ii', a centre), as seen from, or
referred to, the centre of Jupiter.
342
INDEX.
Julian period, calendar and style, '
443-
Jupiter, distance from the sun and \
period of revolution, 134, 139 ; j
diameter, 140 : volume, mass, and '
density, 147 : polar compression, j
255 ; description of, 263 et seq. ;
satellites, 267.
Kepler's laws, 614 ; proofs of, 619
et seq.
Kircnhoff's investigations on spec-
tra, 492.
Latitude (latitude, breadth), terres-
trial, 160 ; how obtained, 560 ; celes-
tial, 360 : how obtained, 554 ; latitude
of a place is equal to the altitude of
the pole, 336 ; Geocentric, Helio-
centric, Jovicentric, Saturnicentric,
latitude as reckoned from the centres
of the planets named.
Lens, its action on a ray of light,
458 ; convex and concave, 462 ; bi-
convex and bi-concave, &c. 463 ;
axis of a, 458 ; achromatic lenses,
464 ; chromatic and spherical aberra-
tion of, 465.
IiC Verrier discovers Neptune, 277.
Libration of the moon, 214.
Light, what it is, 448 ; velocity of,
16, 449 ; aberration of, 449 ; refrac-
tion and reflection, 450 et seq. ; dis-
persion, 465.
Limb, the edge of the di-4t of the
moon, sun, or a planet.
Line, of collimation, 518 ; of nodes,
the imaginary line between the as-
cending and descending node of an
orbit.
Longitude (longitndo, length), ter-
restrial, 161 ; how determined, 5=4;
celestial, 360 ; how determined, 563
et seq. ; mean, the angular distance
from the first point of Aries of a
planet or comet, supposed to move
with a mean rate of motion ; Geo-
centric, Heliocentric, Jovicentric, or
Saturnicentric, longitude as reckoned
from the centres of the planets
named.
Lumiere cendree, 217.
Lunar distances, u-ed to deter-
mine terrestrial longitudes, 565.
Lunation \lunatio], the period of
the moon's journey round the earth,
434-
Luni-solar precession, see Prec(
sion.
Magellanic clouds, 33.
Magnitudes of stars, 22, 23.
Major axis, see Axis.
Maps of countries, how constructe
572-
Mars, 134 ; distance from the sun
and period of revolution, 139 ;
diameter, 140 ; volume, mass, and
density, 147 ; polar compression,
255 ; description of, 256 ; seasons,
262 ; how presented to the earth in
different parts of its orbit, 393 ; how
its distance from the earth is deter-
mined, 583.
Mass. The mass of a heavenly body
is the quantity of matter it contains :
of sun, 103 ; of planets, 147.
Mean distance of a planet, &c. is
half the sum of the aphelion and peri-
helion distances. This is equal to
the semi-axis major of an elliptic
orbit, 139 ; mean anomaly, see Ano-
maly ; mean obliquity is the obliquity
unaffected by nutation ; mean time,
see Time ; mean sun, 405.
Medium, resisting, 297.
Mercury, 134 ; distance from sun
and period of revolution, 139: dia-
meter, 140 ; volume, mass, and den-
sity, 147 ; polar compression, 255 ;
elongation of, 380.
Meridian (tneridies, midday), the
great circle of the heavens passing
through the zenith of any place and
the poles of the celestial sphere, 162.
Metals and metalloids, list of, 207 ;
present in the sun and stars, 10.
Meteors, luminous, their position in
the system, 134 ; divisions of, 298 ;
numbers seen in a star-shower, ib. ;
explanation of star-showers, 301 et
seq. ; the November ring, 308 ;
radiant point, 305 ; cau^e of bril-
liancy, 310 ; shape of orbits, 308,
312; weight of, 311; velocity of,
310 ; detonating meteors, meteoric
irons and stones, 313 ; meteorites,
aerolites, aerosiderites, and aeroside-
rolites, 314 ; sporadic meteors, 315 ;
remarkable meteoric falls, 316 ;
chemical constitution, 317 et seq.
Micrometer (/A««por, small, and
uerpof, measure), an instrument with
fine moveable wires attached to eye-
INDEX.
343
pieces to measure small angular dis-
tances, 473, 519.
Microscopes, 518.
Midnight Sun, 171.
Milky Way, 28; stars increase in
number as they approach, 29 ; ne-
bulae do not, 95.
Miller, Dr. W. A., his spectroscopic
observations, 504.
Minor axis, see Axis.
Minor planets, how discovered,
280, 284 ; sizes, 281 ; orbits and
distances from the sun, 282 ; eccen-
tricity of -orbits, 283 ; brilliancy,
284 ; atmospheres, 286.
Month, the, 434.
Moon, why its shape changes, 12 ;
dimension and distance of, 2 11-12; line
of revolution, 213; libration, 214
nodes, 215, 244 ; moon's path con
cave with respect to the earth, 216
earth-shine, 217 ; brightness of, 218
description of surface, 221 et seq.
rotation, 228 ; no atmosphere, 227
phases, 229 ; eclipses, 233 et seq. ,
apparent motions, 370 et seq. ; har-
vest moon, 372 ; how the distance of
the moon is determined, 579 ; ele-
ments of the moon, see Appendix,
Table V.
Morning star, 380.
Motion, proper, of stars, 43 ; appa-
rent, of planets, 374 et seq. ; direct,
381 ; retrograde, 381 ; laws of, 399
et seq. ; circular, 622.
Mountains, lunar, heights of, 224.
Nadir (natara, to correspond), 328.
Neap tides, 660.
Nebulae, why so called, 6, 76 ; are
probably masses of gas, 13, 96;
classification of, 81 ; light of, 92 ;
variability of, 94 ; spectrum analysis
of the, 498, 501 et seq.
Nebular hypothesis, 98, 210.
Nebulous stars, see Stars.
Neptune, distance from the sun
and period of revolution, 134, 139 ;
diameter, 140 ; volume, mass, and
density, 147 ; discovery of, 277 et
seq.
Node (nodus, a knot), the points at
which a comet's or planet's orbit in-
tersects the plane of the ecliptic : one
is termed the ascending, the other
the descending node, 215. Longitude
of the, one of the elements of an
orbit. It is the angular distance of
the node from the first point of
Aries.
Nubeculae. 33.
Nucleus (Lat. kernel,, of a comet,
291, 293 ; of sun-spots, no.
Nutation (nutatio, a nodding), an
oscillatory movement of the earth's
axis due to the moon's attraction on
the equatorial protuberance, 654 et
seq.
Object-glass of telescopes, con-
struction of, 466 ; aperture and illu-
minating power of, 470 ; accuracy
required in constructing, 480 ; largest
object-glass, 481.
Obliquity of the ecliptic, see Ecliptic.
Occulation (occultare, to hide),
the eclipsing of a star or planet by
the moon or another planet.
Opposition. A superior planet is
in opposition when the sun, earth,
and the planet are on the same
straight line and the earth in the
middle, 378.
Optical double stars, see Stars.
Orbit (orbis, a circle), the path of
a planet or comet round the sun, or
of a satellite round a primary, 282.
Ordnance Survey of England, 570.
Orion, 353.
Parabola, a section of a cone
parallel to one of its sides, 624.
Parabolic orbits of comets, 288.
Par all ac tic inequality, an irregu-
larity in the moon's motion, arising
from the difference of the sun's
attraction at aphelion and peri-
helion.
Parallax (7rap«A\«f«-, a change),
542 ; corrections for, 543, 544 ; equa-
torial horizontal, 543 ; of the moon,
580 ; of Mars, 583 ; of the sun, 585 et
seq. ; old and new values of, 593 ;
of the stars, 594.
Parallels of latitude, 162 ; of de-
clination, 328.
Penumbra (peiie, almost, and
umbra, a shadow), the half-shadow
which surrounds the deeper shadow
of the earth, 237 ; of sun - spots,
no.
Perigee (itfoi, near, and 7^, the
earth), (i) The point in the moon's
orbit* nearest the earth, 212; (a) the
344
INDEX.
position in which the sun or other
body is nearest the earth.
Perihelion (irept, near, and ^««>v),
the point in an orbit nearest the sun,
167 ; distance, the distance of a
heavenly body from the sun at its
nearest approach : longitude of, one
of the elements of an orbit ; it
is the angular distance of the peri-
helion point from the first point of
Aries : passage, the time at which
a heavenly body makes its nearest
approach to the sun, 3.
Peri- Jove, Saturnium, &c., the
nearest approach of a satellite to
the primary named, Jupiter, Saturn,
&c.
Period (irepl, round, and 6<56c, a
path), or periodic time, the time of
a planet's, comet's, or satellite's
revolution ; synodic, the time in
which a planet returns to the same
position with regard to the sun and
earth, 384.
Perturbations (perturbare, to in-
terfere with), the effects of the
attractions of the planets, comets,
and satellites upon each other, con-
sisting of variations in their motions
and orbits described round the sun,
633
Phases (^cio-<c, an appearance), the
various appearances presented by
the illuminated portions of the moon,
(2291 and inferior planets (377) in
various parts of their orbit with regard
to the earth and sun.
Photography, solar, 114; celestial,
507-
Photospheres of the stars, 65 ;
sun, no.
Physical constitution of the stars,
65, 69 ; of the sun, 119 et seq.
Plane of the ecliptic, 105, 136, 300.
Planet (7rAav«-rr|9, a wanderer), a
cool body revolving round a central
incandescent one.
Planets change their positions with
regard to the stars, 4 ; what they
are, n ; names of, 134 ; travel round
the sun in elliptical orbits, 135, 377 ;
and in one direction, 138 ; distances
of, from the sun, 139 ; periods of
revolution, 139 ; real sizes of, 140 ;
comparative sizes of, 141 ; mass,
volume, and density, 144—47 • com-
pared with the earth, 251 et seg. ;
apparent movements of, 374 et seq. ;
varying distances from the earth,
376 ; brilliancy and phases, 377 ;
inferior and superior, 378 ; conjunc-
tion and opposition, 378 ; elonga-
tions, 380 ; direct and retrograde
motion, 381 ; stationary points, 382 ;
synodic periods, 384 ; inclinations
and nodes of orbits, 388; apparent
paths among the stars, 391 et seq. ;
elements of the. see Appendix.
Table II.
Planetary nebulae, see Nebulae.
Plateau's experiment, 197.
Pointer.*, the, 341.
Polar axis of the earth, 153, 163 ;
compression (see Comoression), 255 ;
distance, 329.
Polaris (Lat.), the pole-star, 341 ; is
not always the same, 547.
Poles (TroXeu), I turn), the extremi-
ties of the imaginary axis on which
the celestial bodies rotate, 153, 261 ;
the poles of the heavens, 328 ; are
the extremities of the axis of the
celestial sphere which is parallel to
the earth's axis ; the poles of the
ecliptic are the extremities of the
axis at right angles to the plane of
the ecliptic, 360 ; of the earth,
J53-
Position-Circle (of micrometers),
5i9-
Precession (fnecedere, to precede)
of the equinoxes, or luni-solar pre-
cession, a slow retrograde motion
of the equinoctial points upon the
ecliptic, 361, 548 ; cause of, explained,
645 et seq.
Prime, vertical, see Vertical.
Prisms refract light, 453
Prominences, red, of the sun, 118.
Proper motion, see Motion.
Quadrant (quadrans, a fourth part),
the fourth part of the circumference
of a circle or 90°; of altitude, a
flexible strip of brass graduated into
90°, attached to the celestial globe
for determining celestial latitudes,
declinations being determined by the
brass meridian.
Quadrature. Two heavenly bodies
are said to be in quadrature when
there is a difference of longitude of
90° between them. Thus the moon
INDEX.
315
is in quadrature with respect to the
sun at the first and last quarters.
Quarters of the moon, 231.
Radiant point of shooting stars,
305-
Radiation, solar, 124 et seq.
Radius (Lat. a spoke of a wheel)
vector, an imaginary line joining
the sun and a planet or comet in any
point of its orbit, 615.
Red prominences and flames, 118,
248.
Reflecting telescope, or reflector,
481.
Reflection, 451.
Refracting telescope, or refractor,
see Telescope.
Refraction (refrangere, to hend),
atmospheric, 450, 453 ; of light by
prisms, 453 ; index of, 453.
Resisting medium, see Medium.
Retrogradation, arc of. The arc
apparently traversed by planets
while their motion is retrograde,
381.
Retrograde motion, see Motion.
Revolution, the motion of one
body round another, 12 ; time of,
the period in which a heavenly body
returns to the same point of its
orbit ; the revolution may either be
1 anomalistic if measured from the
aphelion or perihelion points, sidereal
with reference to a star, synodical
with reference to a node, or tropical
with reference to an equinox or
tropic.
Right ascension, see Ascension,
Right.
Rilles on the moon, 226.
Rings of Saturn, see Saturn.
Rocks, list of terrestrial, 183.
Rotation, the motion of a body
round a central axis : of sun, 104 ;
of earth, 153 ; of moon, 214; possibly
slackening, 667
Rutherford, Mr., his lunar, photo-
graph, 507.
Saros, a term applied by the Chal-
deans to the cycle of eclipses, 244.
Satellite (satellcs, a companion),
a term applied to the smaller bodies
revolving round planets and stars,
137, 142, 267 ; elements of the, see
Appendix, Table 1 1 1.
Saturn, distance from the sun and
period of revolution, 134, 139 ;
diameter, 140; volume, mass, and
density, 147 ; polar compression,
255 ; the rings, 270 et seq. ; dimen-
sion of, 272 ; of what composed,
273 ; appearance of, 274 ; atmo-
sphere, to. ', solar eclipses due to the
rings, 276 ; how presented to the
earth in different parts of its orbit,
Scintillation (scintilla, a spark),
the "twinkling" of the stars.
Seasons of the earth, 169, 175 et
seq. ; of Mars, 254, 262 ; of Jupiter,
254-
Secular [ttdtbtmt an age) inequa-
lities, see Inequalities ; acceleration
of the moon's mean motion, see
Acceleration.
Selenography (o-c\/;i'»i, the moon),
the geography of the moon.
Semi-diurnal arc, see Arc.
Sextant, an instrument consisting
of the sixth part of a circle, finely
graduated, by which, by means of
reflection, the angular distances of
celestial bodies are measured, 520.
Shooting stars, see Meteors, lumi-
nous.
Sidereal (sidus, a star), relating to
the stars ; clock, see Clock ; day, 358 ;
time, see Time.
Signs of the zodiac, see Zodiac.
Snow on Mars, 260.
Solar spectrum, see Spectrum.
Solar system, 133 et seq.
Solstices, or solstitial points (so/,
the sun, and stare, to stand still),
the points in the sun's path at which
the extreme north and south decli-
nations are reached, and at which
the motion is apparently arrested
before the direction of motion is
changed, 171.
Solstitial colure, see Colure.
Sorby'S researches on meteorites,
320.
Spectroscope, 491 ; star spectro-
scope, 505 ; the Kew spectroscope,
506; direct vision, 506.
Spectrum, 454 ; irrationality of the,
458 ; the solar, 487 ; description of,
488; dark lines and bright lines, 490,
491 ; spectrum analysis, 489 et seq. ;
general laws of, 493 ; general results
of, 406-08.
346
INDEX.
Sphere (<r0aip«), celestial, the sphere
of stars which apparently incloses
the earth, i, 326 ; of observation,
329-
Spherical trigonometry, see Trigo-
nometry.
Spheroid, the solid formed by the
rotation of an eclipse on one of its
axes : it is oblate if it rotates on the
minor axis, and prolate if it rotates
on the major axis.
Spring: tides, 660.
Star-showers, see Meteors.
Stars, why invisible in daytime, 2 ;
why they appear at rest, 8 ; why
they shine, 10 ; distance of nearest,
16 ; their distance generally, 25-27 ;
magnitudes of, 22, 23 ; telescopic, 22 :
comparative brightness of, 23; divided
into constellations, 35-41 ; brightest,
42 ; double and multiple, 47-50 ; vari-
able and temporary, 51-59; the sun-
a variable star, 121 ; coloured, 60-
63 ; size of, 64 ; physical constitution
of, 65-69; clusters of, 71, 75 ; appa-
rent movements of, 326 ; positions of,
on celestial sphere, 326 et seq. ; appa-
rent daily movement, 331 et seq. ;
apparent yearly movement, 344 et
seq. \ pole-star, 341 ; zone of, 335 ;
how to observe the, 342, 349 ;
those seen at midnight are opposite
to the sun. 344 et seq. ; constellations
visible throughout the year, 352 et
seq.; circumpolar, 335 ; sidereal day,
358 ; how the elements in the stars
are determined, 493, 495, 497 ; paral-
lax of the stars, 594-95.
Stationary points, those points in
a planet's orbit at which it appears
to have no motion among the stars,
382.
Stellar parallax, see Parallax.
Stones, meteoric, 313.
Styles, old and new, 443 ; of sun-
dials, 402.
Sun, is a star, 9 ; why it shines, ip ;
its relative brilliancy, 23, 100 ; dis-
tance, 101 ; diameter, 101 ; volume,
103 ; mass, 103 ; rotation, 104 ; posi-
tion of axis, 106 ; sun-spots, proper
motion of, 107; description of, no;
size of, 120 ; period of, 120 ; tele-
scopic appearance of, 109 et seq. ;
photosphere, no, 119 ; atmosphere,
119, 123; faculae, 113 ; willow leaves
and granules, 115, 116; red flames,
118 ; elements in the photosphere,
123; how determined by spectrum
analysis, 494-96 ; amount of light,
125 ; heat, 126 ; chemical force, 128 ;
solar radiation, 205 ; eclipses of, 234
et seq ; their phenomena, 240 et seq. ; '
apparent motions, 357 ; solar day,
358 ; motion in the ecliptic, 363 ;
rising and setting and apparent daily
path, 364 ; mean sun, motion of
the, 405 ; how the sun's distance is
determined, 585 et seq. ; old and
new values of the solar parallax,
593 ; solar elements, see Appendix,
Table IV.
Sun-dial, the, 399, 400.
Superior conjunction, see Con-
junction.
Superior planets ? see Planets.
Symbols (vvuftoko*), the name
given to certain signs, used as abbre-
viations, sec Appendix, Table I.
Synodic period, see Period.
Syzigies (avv, with, and fi'-yov, a
yoke), the points in the moon's orbit
at which it is in a line with the earth
and sun, or when it is in conjunction
or opposition.
Tails of comets, 291, 293.
Telescope (r^Ae, afar, and O-KOITMI),
I see), construction of, 467 ; illumi-
nating or space-penetrating power,
90, 469 ; magnifying power, 470 ;
eye-pieces, 471-73 ; object-glass, 466,
470 ; tube, 474 ; powers of, 475; how
to use the, 476-79 ; largest, 481 ;
various mountings, 482; equatorial,
482 ; altazimuth, 486, 521 et seq. ;
transit circle, 486, 524 et seq. ; transit
instrument, 486, 558
Temperature of the sun, 126 ; of
the earth's crust, 193.
Temporary star, see Star.
Terminator, 222.
Tides (tidan, to happen, Saxon), 659
et seq.
Time, how measured, 405 ; the mean
sun, motion of, 408 ; equation of
time, 415 ; apparent and mean solar
day, 419: Greenwich mean time,
421 ; rules for converting solar into
sidereal time, and vice versa, 427,
see Appendix, Tables VII. and VIII. ;
civil, 369; week, 432; month, 434;
year, 436 ; bissextile, 440 ; Julian
and Gregorian calendars (new style
INDEX
347
and old style), 443 ; time required
by light to reach us from the stars,
27 ; from the nebulae, 91 ; how ob-
tained, 558, see Appendix, Tables
VI. VII. and VIII.
Total eclipse, see Eclipses.
Trade winds, 201.
Transit (trans, across, and ire, to
go', the passage (il of a heavenly
body across the meridian of a place
fin the case of circumpolar stars
there is an upper and a lower transit,
the latter sometimes called the tran-
sit snb polo} \ (2) of one heavenly
body across the disc of another, e.g.
the transit of Venus across the sun,
586; of a satellite of Jupiter across
the planet's disc, 267.
Transit circle, 486 ; when used
and general description 0^-524 ; how
used, 525 et seq.
Transit instrument, 486, 558.
Trigonometry, plane and spheri-
cal, 515.
Trigonometrical ratios, 516.
Tropical revolution, see Revolution.
Tropics (rpeTTw, I change) of Can-
cer and Capricorn respectively,
the circles of declination which mark
the most northerly and southerly
points in the ecliptic,* in which the
sun occupies the signs named, 162.
Ultra-zodiacal planets, a name
sometimes given to the minor planets,
because their orbits exceed the limits
of the zodiac.
Umbra (Lat. a shadow}, the darkest
central portion of the shadow cast
by a heavenly body, such as the
moon or earth, is so called : it is sur-
rounded by the penumbra, 237 ;
umbra of sun-spots, no.
Universe, our, one of many, 8 ;
shape of, 30-32.
Uranus, 134 : distance from the
sun and period of revolution, 139 ;
diameter, 140 ; volume, mass, and
density, 147 ; inclination of axis,
254 ; discovery of, 277.
Vapour, aqueous, 209.
Variable star, see Stars ; nebulae,
see Nebulae.
1 Variation of the moon, one of the
lunar inequalities.
Venus, 134 ; distance from the sun
and period of revolution, 139 ; dia-
meter, 140 ; volume, mass, and den-
sity, 147 ; polar compression, 255 ;
a morning and evening star by turns,
380; transits of, across the sun's
disc, 582, 586 ct seq. ; the transit of
1882, 591.
Vernier. 518.
Vertical (vertex, the top). A vertical
line (329) is a line perpendicular to
the surface of the eaith at anyplace,
and is directed therefore to the
zenith ; a vertical circle is one that
passes through the zenith and nadir
of the celestial sphere, 329 ; the
prime vertical (329) is the vertical
circle passing through the east and
west points of the horizon.
Via Lactea, see Milky Way.
Volume (volumen, bulk) is the cubi-
cal contents of a celestial body ; of
the sun, 103; of the planets, 147.
Week, names of.the days of the, 482.
Weight, what it is, 602.
Willow leaves in the penumbra
ot sun-spots, 116'.
"Winds, 202.
Wire micrometer, see Micrometer.
Year, 164, 436 ; length of the planets'
years, 253.
Zenith, the point of the celestial
sphere overhead, 328 ; distance, 329.
Zodiac, the portion of the heavens
extending 9° on either side of the
ecliptic, in which the sun and major
planets appear to perform their
annual revolutions, 37, 361. It is
divided into twelve parts, termed
signs of the zodiac. These signs
were named after the constellations
which occupied them in the time of
Hipparchus.
Zodiacal light, 134; constellations,37.
Zones, torrid, frigid, and temperate,
of the earth, 162 ; of stars, 335.
LONDON :
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LESSONS IN ELEMENTARY PHYSIOLOGY.
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LESSONS IN ELEMENTARY CHEMISTRY,
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With numerous Illustrations and Chromo-Litho. of the Solar
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LESSONS IN ELEMENTARY BOTANY.
The part on Systematic Botany based upon material left in
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By DANIEL OLIVER, F.R.S., F.L.S.,
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ELEMENTARY LESSONS IN PHYSICAL
GEOLOGY.
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{Preparing
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MACMILLAN & CO. LONDON.
OCTOBER, 1868.
LIST OF EDUCATIONAL BOOKS
PUBLISHED BY
MACMILLAN AND CO.,
1 6, BEDFORD STREET, CO VENT GARDEN,
, w.c.
CONTENTS.
Page
CLASSICAL 3
MATHEMATICAL 7
SCIENCE ... 17
MISCELLANEOUS 19
DIVINITY 21
BOOKS ON EDUCATION 24
MESSRS. MACMILLAN & Co. beg to call attention to the
accompanying Catalogue of their EDUCATIONAL WORKS,
ihe writers of which are mostly scholars of eminence in the
Universities, as well as of large experience in teaching.
Many of the works have already attained a wide
circulation in England and in the Colonies, and are
acknowledged to be among the very best Educational Books
on their respective subjects.
The books can generally be procured by ordering them
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time diffictilty should arise, Messrs. MACMILLAN will feel
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Notices of errors or defects in any of these works will
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LIST OF EDUCATIONAL BOOKS.
CLASSICAL.
^SCHYLI EUMENIDES. The Greek Text, with English Notes,
and English Verse Translation and an Introduction. By BERNARD
DRAKE, M.A., late Fellow of King's College, Cambridge. 8vo.
7J. 6d.
The Greek Text adopted in this Edition is based upon that of Wellauer,
which may be said in general terms to represent that of the best manu-
scripts. But in correcting the Text, and in the Notes, advantage has been
taken of the suggestions of Hermann, Paley, Linwood, and other com-
mentators.
ARISTOTLE ON FALLACIES; OR, THE SOPHISTICI
ELENCHI. With a Translation and Notes by EDWARD POSTE,
M.A., Fellow of Oriel College, Oxford. 8vo. Ss. 6d.
Besides the doctrine of Fallacies, Aristotle offers either in this treatise, or
in other passages quoted in the commentary, various glances over the
world of science and opinion, various suggestions on problems which are
still agitated, and a vivid picture of the ancient system of dialectics, which
it is hoped may be found both interesting and instructive.
" It is not only scholarlike and careful ; it is also perspicuous." — Guardian.
ARISTOTLE.— AN INTRODUCTION TO ARISTOTLE'S
RHETORIC. With Analysis, Notes, and Appendices. By
E. M. COPE, Senior Fellow and Tutor of Trinity College, Cam-
bridge. 8vo. 14^.
This work is introductory to an edition of the Greek Text of Aristotle's
Rhetoric, which is in course of preparation.
" Mr. Cope has given a very useful appendage to the promised Greek Text ;
but also a work of so much independent use that he is quite justified in his
separate publication. All who have the Greek Text will find themselves
supplied with a comment ; and those who have not will find an analysis of
the work." — Atlienteum.
EDUCATIONAL BOOKS.
CATULLI VERONENSIS LIBER, edited by R. ELLIS, Fellow of
Trinity College, Oxford. i8mo. 3^. 6d.
" It is little to say that no edition of Catullus at once so scholarlike has ever
appeared in England." — Athenceum.
" Rarely have we read a classic author with so reliable, acute, and safe a
guide." — Saturday Review.
CICERO.— THE SECOND PHILIPPIC ORATION. With an
Introduction and Notes, translated from the German of KARL
HALM. Edited, with Corrections and Additions, by JOHN E. B.
MAYOR, M.A., Fellow and Classical Lecturer of St. John's Col-
lege, Cambridge. Third Edition, revised. Fcap. 8vo. 5J-.
"A very valuable edition, from which the student may gather much both in
the way of information directly communicated, and directions to other
sources of knowledge." — Athenceum.
DEMOSTHENES ON THE CROWN. The Greek Text with
English Notes. By B. DRAKE, M.A.; late Fellow of King's
College, Cambridge. Third Edition, to which is prefixed
^ESCHINES AGAINST CTESIPHON, with English Notes. Fcap.
8vo. 5J.
The terseness and felicity of Mr. Drake's translations constitute perhaps
the chief value of his edition, and the historical and archaeological details
necessary to understanding the De Corona have in some measure been
anticipated in the notes on the Oration of yEschines. In both, the text
adopted in the Zurich edition of 1851, and taken from the Parisian MS.,
has been adhered to without any variation. Where the readings of
Bekker, Dissen, and others appear preferable, they are subjoined in the
notes.
HODGSON.— MYTHOLOGY FOR LATIN VERSIFICATION.
A Brief Sketch of the Fables of the Ancients, prepared to be
rendered into Latin Verse for Schools. By F. HODGSON, B.D.,
late Provost of Eton. New Edition, revised by F. C. HODGSON,
M.A. i8mo. 3-r.
Intending the little book to be entirely elementary, the Author has made it
as easy as he could, without too largely superseding the use of the Dic-
tionary and Gradus. By the facilities here afforded, it will be possible, in
many cases, for a boy to get rapidly through these preparatory exercises ;
and thus, having mastered the first difficulties, he may advance with better
hopes of improvement to subjects of higher character, and verses of more
difficult composition.
CLASSICAL.
JUVENAL, FOR SCHOOLS. With English Notes. By J. E. B.
MAYOR, M.A. New and Cheaper Edition. Crown 8vo.
[In the Press.
" A School edition of Juvenal, which, for really ripe scholarship, extensive
acquaintance with Latin literature, and familiar knowledge of Continental
criticism, ancient and modern, is unsurpassed, we do not say among Eng-
lish School-books, but among English editions generally." — Edinburgh
Review.
.— THE COMUS of MILTON rendered into Greek
Verse. By LORD LYTTELTON. Extra fcap. 8vo. Second Edition.
— THE SAMSON AGONISTES of MILTON rendered into
Greek Verse. By LORD LYTTELTON. Extra fcap. 8vo. 6s. 6d.
MARSHALL.— K TABLE OF IRREGULAR GREEK VERBS,
Classified according to the Arrangement of Curtius's Greek
Grammar. By J. M. MARSHALL, M.A., Fellow and late Lec-
turer of Brasenose College, Oxford ; one of the Masters in Clifton
College. 8vo. cloth, is.
MA YOR.— FIRST GREEK READER. Edited after KARL HALM,
with Corrections and large Additions by JOHN E. B. MAYOR, M.A.,
Fellow and Classical Lecturer of St. John's College, Cambridge.
Fcap. 8vo. 6s.
MERIVALE.—KEKTS HYPERION rendered into Latin Verse.
By C. MERIVALE, B.D. Second Edition. Extra fcap. 8vo.
J. 6d.
PLA7V.—THE REPUBLIC OF PLATO. Translated into En-
glish, with an Analysis and Notes, by J. LI. DA VIES, M.A., and
D. J. VAUGHAN, M.A. Third Edition, with Vignette Portraits
of Plato and Socrates, engraved by JEENS from an Antique Gem.
i8mo. 4$-. 6d.
ROBY.—K LATIN GRAMMAR for the Higher Classes in Grammar
Schools. By H. J. ROBY, M.A. ; based on the "Elementary
Latin Grammar." \_InthePress.
EDUCATIONAL BOOKS.
SALLUST.—CAIl SALLUSTII CRISPI Catilina et Jugurtha.
For use in Schools (with copious Notes). By C. MERIVALE, B.D.
(In the present Edition the Notes have been carefully revised, and
a few remarks and explanations added.) Second Edition. Fcap.
8vo. 4-r. 6d.
The Jugurtha and the Catilina may be had separately, price 2s. 6d.
each.
TACITUS.— THE HISTORY OF TACITUS translated into ENG-
LISH. By A. J. CHURCH, M.A., and W. J. BRODRIBB, M.A.
With Notes and a Map. 8vo. los. 6d.
The translators have endeavoured to adhere as closely to the original as was
thought consistent with a proper observance of English idiom. At the
same time it has been their aim to reproduce the precise expressions of the
author. The campaign of Civilis is elucidated in a note of some length
which is illustrated by a map, containing only the names of places and of
tribes occurring in the work.
- THE AGRICOLA and GERMANY. By the same translators.
With Maps and Notes. Extra fcap. 8vo. 2s. 6d.
THRING.— Works by Edward Thring, M.A., Head Master of
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— A CONSTRUING BOOK. Fcap. 8vo. 2s. 6d.
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serted as the passages go on, are printed in Italics. It is hoped by this
plan that the learner, whilst acquiring the rudiments of language, may
store his mind with good poetry and a good vocabulary.
- A LATIN GRADUAL. A First Latin Construing Book for
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The main plan of this little work has been well tested.
The intention is to supply by easy steps a knowledge of Grammar, combined
with a good vocabulary ; in a word, a book which will not require to be
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A short practical manual of common Mood constructions, with their English
equivalents, form the second part.
— A MANUAL of MOOD CONSTRUCTIONS. Extra fcap.
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THUCYDIDES.—TVLE SICILIAN EXPEDITION. Being Books
VI. and VII. of Thucydides, with Notes. A New Edition, revised
and enlarged, with a Map. By the Rev. PERCIVAL FROST, M'.A.,
late Fellow of St. John's College, Cambridge. Fcap. 8vo. 5^.
This edition is mainly a grammatical one. Attention is called to the force
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MA THE MA TICAL.
WRIGHT.— Works by J. Wright, M.A., late Head Master of
Sutton Coldfield School : —
— HELLENICA ; Or, a HISTORY of GREECE in GREEK,
as related by Diodorus and Thucydides, being a First Greek
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In the last twenty chapters of this volume, Thucydides sketches the rise and
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Greek.
— A HELP TO LATIN GRAMMAR ; Or, the Form and Use
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4^. 6d.
" Never was there a better aid offered alike to teacher and scholar in that
arduous pass. The style is at once familiar and strikingly simple and
lucid ; and the explanations precisely hit the difficulties, and thoroughly
explain* them." — English Journal of Education.
— THE SEVEN KINGS OF R9ME. An Easy Narrative,
abridged from the First Book of Livy by the omission of difficult
passages, being a First Latin Reading Book, with Grammatical
Notes. Fcap. 8vo. $s.
This work is intended to supply the pupil with an easy Construing-book,
which may at the same time be made the vehicle for instructing him in
the rules of grammar and principles of composition. Here Livy tells his
own pleasant stories in his own pleasant words. Let Livy be the master
to teach a boy Latin, not some English collector of sentences, and he will
not be found a dull one.
— A VOCABULARY AND EXERCISES on the "SEVEN
KINGS OF ROME." Fcap. 8vo. 2s. 6d.
The Vocabulary and Exercises may also be had bound up with
"The Seven Kings of Rome," price 5-r.
MATHEMATICAL.
AIRY.— Works by G. B. Airy, Astronomer Royal : —
— ELEMENTARY TREATISE ON PARTIAL DIFFEREN-
TIAL EQUATIONS. Designed for the use of Students in the
University. With Diagrams. Crown 8vo. cloth, $s. 6d.
It is hoped that the methods of solution here explained, and the instances
exhibited, will be found sufficient for application to nearly all the important
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tion the aid of partial differential equations.
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— ON SOUND and ATMOSPHERIC VIBRATIONS. With
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3AYMA.—THE ELEMENTS of MOLECULAR MECHANICS.
By JOSEPH BAYMA, S.J., Professor of Philosophy, Stonyhurst
College. Demy 8vo. cloth, los. 6d.
BOOLE.— Works by Gr. Boole, D.C.L., F.R.S., Professor of
Mathematics in the Queen's University, Ireland : —
— A TREATISE ON DIFFERENTIAL EQUATIONS. New
and Revised Edition. Edited by I. TODHUNTER. Crown 8vo.
cloth, I4J-.
The author has endeavoured in this Treatise to convey as complete an ac-
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Equations, as was consistent with the idea of a work intended primarily
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that kind of matter which has usually been thought suitable to the beginner,
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This work is in some measure designed as a sequel to the Treatise oti
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MA THEM A TICAL.
BEASLEY.—AN ELEMENTARY TREATISE ON PLANE
TRIGONOMETRY. With Examples. By R. D. BEASLEY,
M.A., Head Master of Grantham Grammar School. Second
Edition, revised and enlarged. Crown 8vo. cloth, 3^. 6d.
This Treatise is specially intended for use in Schools. The choice of matter
has been chiefly guided by the requirements of the three days' Examina-
tion at Cambridge, with the exception of proportional parts in Logarithms,
which have been omitted. About Four hundred Examples have been
added, mainly collected from the Examination Papers, of the last ten years,
and great pains have been taken to exclude from the body of the work any
which might dishearten a beginner by their difficulty.
CAMBRIDGE SENATE-HOUSE PROBLEMS and RIDERS,
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CAMBRIDGE COURSE OF ELEMENTARY NATURAL PHI-
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J. C. SNOWBALL, M.A., late Fellow of St. John's College. Fifth
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CAMBRIDGE AND DUBLIN MA THEMA TICAL JOURNAL.
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CHEYNE.— AN ELEMENTARY TREATISE on the PLANET-
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— THE EARTH'S MOTION of ROTATION. By C. H. H.
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io EDUCATIONAL BOOKS.
CtfSLDE.—THE SINGULAR PROPERTIES of the ELLIPSOID
and ASSOCIATED SURFACES of the Nth DEGREE. By
the Rev. G. F. CHILDE, M.A., Author of "Ray Surfaces,"
"Related Caustics," &c. 8vo. icxr. 6d.
CHRISTIE,— A COLLECTION OF ELEMENTARY TEST-
QUESTIONS in PURE and MIXED MATHEMATICS ; with
Answers and Appendices on Synthetic Division, and on the
Solution of Numerical Equations by Horner's Method. By JAMES
R. CHRISTIE, F.R.S., late First Mathematical Master at the
Royal Military Academy, Woolwich. Crown 8vo. cloth, &r. 6d.
D ALTON.— ARITHMETICAL EXAMPLES. Progressively ar-
ranged, with Exercises and Examination Papers. By the Rev.
T. D ALTON, M.A., Assistant Master of Eton College. i8mo.
cloth. 2s. 6d.
DAY.— PROPERTIES OF CONIC SECTIONS PROVED
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By the Rev. H. G. DAY, M.A., Head Master of Sedbergh Grammar
School. Crown 8vo. 3«r. 6d.
DODGSON.—AN ELEMENTARY TREATISE ON DETER-
MINANTS, with their Application to Simultaneous Linear Equa-
tions and Algebraical Geometry. By C. L. DODGSON, M.A.,
Mathematical Lecturer of Christ Church, Oxford. Small 4to.
cloth, i or. 6d.
DREW— GEOMETRICAL TREATISE on CONIC SECTIONS.
By W. H. DREW, M.A., St. John's College, Cambridge. Third
Edition. Crown 8vo. cloth, qs. 6d.
In this work the subject of Conic Sections has been placed before the student
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may find it an easy and interesting continuation of his geometrical studies.
With a view also of rendering the work a complete Manual of what is re-
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or inserted among the examples, every book-work question, problem, and
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present time.
— SOLUTIONS TO THE PROBLEMS IN DREW'S CONIC
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FERRERS.— AN ELEMENTARY TREATISE on TRI LINEAR
CO-ORDINATES, the Method of Reciprocal Polars, and the
Theory of Projections. By the Rev. N. M. FERRERS, M.A.,
Fellow and Tutor of Gonville and Caius College, Cambridge.
Second Edition. Crown 8vo. 6s. 6d.
The object of the author in writing on this subject has mainly been to place
it on a basis altogether independent of the ordinary Cartesian system, in-
stead of regarding it as only a special form of Abridged Notation. A short
chapter on Determinants has been introduced.
MA THEM A TICAL. 1 1
FROST.— THE FIRST THREE SECTIONS of NEWTON'S
PRINCIPIA. With Notes and Illustrations. Also a Collection
of Problems, principally intended as Examples of Newton's
Methods. By PERCIVAL FROST, M.A., late Fellow of St. John's
College, Mathematical Lecturer of King's College, Cambridge.
Second Edition. 8vo. cloth, los. 6d.
The author's principal intention is to explain difficulties which may be en-
countered by the student on first reading the Principia, and to illustrate
the advantages of a careful study of the methods employed by Newton, by
showing the extent to which they may be applied in the solution of prob-
lems ; he has also endeavoured to give assistance to the student who is
engaged in the study of the higher branches of Mathematics, by repre-
senting in a geometrical form several of the processes employed in the
Differential and Integral Calculus, and in the analytical investigations of
Dynamics.
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MATHEMATICAL. 13
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MATHEMATICAL. 15
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SCIENCE. 17
WILSON.— ELEMENTARY GEOMETRY. PART I. Angles,
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MISCELLANEOUS. 19
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DIVINITY. 21
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and orderly arrangement of the Sacred Story. . . . His work is solidly and
completely done." — Athenceum.
— A SHILLING BOOK of OLD TESTAMENT HISTORY,
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with a Rationale of its Offices. By FRANCIS PROCTER, M.A.
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In the course of the last twenty years the whole question of Liturgical know-
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currency, that the present volume has been put together.
— AN ELEMENTARY HISTORY of the BOOK of COMMON
PRAYER. By FRANCIS PROCTER, M.A. Second Edition.
i8mo. 2s. 6d.
The author having been frequently urged to give a popular abridgment of
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in the larger work are accompanied by elaborate discussions and references
to authorities indispensable to the student. It is hoped that this book may
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the Forms of our Common Prayer.
PSALMS of DAVID Chronologically Arranged. By FOUR FRIENDS.
An amended version, with Historical Introduction and Explanatory
Notes. Crown 8vo., los. 6d.
" It is a work of choice scholarship and rare delicacy of touch and feeling."
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DIVINITY. 23
RAMSA K— THE CATECHISER'S MANUAL; or, the Church
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Schoolmasters, and Teachers. By ARTHUR RAMSAY, M.A.
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S7MPSOJV.—A.N EPITOME of the HISTORY of the CHRIST-
IAN CHURCH. By WILLIAM SIMPSON, M.A. Fourth
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SWAINSON.—K HAND-BOOK to BUTLER'S ANALOGY.
By C. A. SWAINSON, D.D., Norrisian Professor of Divinity at
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WESTCOTT.— K GENERAL SURVEY of the HISTORY of the
CANON of the NEW TESTAMENT during the First Four
Centuries. By BROOKE Foss WESTCOTT, B.D., Assistant Master
at Harrow. Second Edition, revised. Crown 8vo. los. 6d.
The Author has endeavoured to connect the history of the New Testament
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— INTRODUCTION to the STUDY of the FOUR GOSPELS.
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- THE BIBLE in the CHURCH. A Popular Account of the
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Churches. Second Edition. By BROOKE Foss WESTCOTT, B.D.
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WILSON.— AN ENGLISH HEBREW and CHALDEE LEXI-
CON and CONCORDANCE to the more Correct Understanding
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the Original Hebrew. By WILLIAM WILSON, D.D., Canon of
Winchester, late Fellow of Queen's College, Oxford. Second
Edition, carefully Revised. 4to. cloth, 25^.
The aim of this work is, that it should be useful to Clergymen and all per-
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24 BOOKS ON EDUCATION.
BOOKS ON EDUCATION.
ARNOLD.— A FRENCH ETON ; or, Middle-Class Education and
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BLAKE.— A VISIT to some AMERICAN SCHOOLS and COL-
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ESSAYS ON A LIBERAL EDUCATION.' By CHARLES STUART
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FARRAR.— ON SOME DEFECTS IN PUBLIC SCHOOL
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THRING.— EDUCATION AND SCHOOL. By the Rev. EDWARD
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YOUMANS.— MODERN CULTURE : its True Aims and Require-
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